Download B-Tech Lab Manual - Bapatla Engineering College

BAPATLA ENGINEERING
COLLEGE::BAPATLA
(AUTONOMOUS)
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Department of Physics
Laboratory Manual
Engineering Physics
PHL 101 & PHL201
¼ B.TECH PHYSICS LAB MANUAL
CYCLE-1
1. COMPOUND PENDULUM
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2. MAGNETIC FIELD ALONG THE AXIS OF A CURRENT CARRYING
CIRCULAR COIL.
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3. NEWTON RINGS
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4. SOLAR CELL
CYCLE-2
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5. DETERMINATION OF ENERGY GAP OF A SEMICONDUCTOR
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6. HALL EFFECT
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7. RESONANCE IN L-C-R CIRCUIT
8. DIFFRACTION GRATING
9. CHARACTESTICS OF A PHOTO CELL
10.DETERMINATION OF WAVELENGTH OF LASER LIGHT BY
DIFFRACTION GRATING
Name of the student____________________ Branch & Roll No
LIST OF EXPERIMENTS
INDEX
Name of the experiment
Page numbers
1
Compound pendulum
1- 3
2
Torsional pendulum
4-5
3
Sonometer
6-7
4
Newton rings
8-9
5
Diffraction Grating
10-11
6
Air wedge
7
Dispersive power of a prism
8
Wavelength of LASER diode
9
Photo cell
10
Solar cell
12-13
14-16
17
18-19
20-21
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S.No
Field along the axis of a circular coil
22-23
Platinum resistance thermometer
24-26
13
Forbidden energy gap of semiconductor
27-29
14
Hall effect
30-32
15
Cathode ray oscilloscope
33-34
16
Resonance in LCR circuit
35-36
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COMPOUND PENDULUM
AIM :To determine acceleration due to gravity ( g )at a place using compound pendulum.
APPARATUS: Compound pendulum, knife edges, telescope, stop watch, meter scale.
DEFINATION OF g : When a body is left to free fall, then it acquires a constant acceleration andmove
to a ds ea th, due to ea th s g a itatio . No the o sta t a ele atio a ui ed that f eel falli g od
is called acceleration due to gravity.
FORMULA: Time period of oscillation of a physical pendulum or compound pendulum is given by
=
√
+
Compare the above formula with time period of oscillation of a simple pendulum. i.e.
Here
= √
+
√
=
is alled le gth of e ui ale t si ple pe dulu . K is adius of g atio ; D is dista e of the
cm/s2
at
�
et ee
ap
From the above formula acceleration due to gravity is given by � =
a g aph d a
la
poi t of suspe sio f o e te of g a it . The alue of L is esti ated f o
distance of point of suspension ( ) verses time period of oscillation (T)
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THEORY:
In lower classes you might be familiar with simple pendulum experiment for the determination of
acceleration due to gravity, hence before to do this experiment one has to know the difference between
simple pendulum, and compound pendulum experiment, oth of the
e e ea t fo dete i atio of g
value. They are
1. Simple pendulum is an ideal case, because it require a point mass object
2. It requires torsion less string.
The above mentioned two conditions are not practically possible, hence it is only a mathematical ideal case,
and whereas compound pendulum is a physical pendulum.
A rigid body of any shape which is free to oscillate without any friction on a vertical plane is called
compound pendulum. It swings harmonically back and forth about a verticalz-axis (Passing through
point O as sho i Fig , he o pou d pe dulu is displaced from its equilibrium position by an
angle . In the equilibrium position, the center of gravity of the body is vertically below at a distance
of OG. Let the mass of the body is m, In this experiment you are going to measure theacceleration
due to gravity, g by observing the motion of a compound pendulum. Let us consider acompound
pendulum shown in figure 1.
Pull the compound pendulum through an angle
totorque acting on it, given by
and release it, then it makes angular oscillations due
�
⃗ =⃗ ⃗
�
⃗ = ⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗⃗⃗
�
⃗⃗ = −
−−−−
Here –ve sign is because of force and displacement is opposite to each other.
For small amplitudes
≈
Now expression (1) becomes ⃗⃗� = −
We know that torque �
⃗⃗ =
[
]
� =
=−
=>
+(
)
=
−−−−
Here is the o e t of i e tia of pe dulu , a out a a is passi g th ough poi t O .
Equation (2) represents simple harmonic equation of the form, i.e.
+�
=
Here �is angular frequency of simple pendulum. From comparison with Eq (2), we can write
�= √
=√
=>� =
=> =
−−−−
√
+
√
=
+
−−−−−
rin
g
√
=
ee
Thus
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According to parallel axes theorem, the rotational moment of inertia, about any axis parallel to the one
passing the center of gravity is given by
=
+
−−−
We k o that o e t of i e tia a out a a is passi g th ough e te of g a it G , gi e
=
He e K is adius of g atio of the od a out a a is passi g th ough G .
=
+
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√
=
+
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This suggests that
=
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n
Comparing expression (5) with expression for time period of simple pendulum i.e.
−−−−
=
=
fP
OG p odu ed su h that
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The term L is called length of equivale t si ple pe dulu .
This is e ause si ple pe dulu of le gth L is ha i g a ti e pe iod, sa e as that of ti e pe iod of
compound pendulum. Also it seems that all the mass of the body were concentrated at point “ , along
+
=
+
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The poi t “ is alled e te of os illatio . I a alog
entire mass is concentrated at that point.
=
ar
From expression (6), the extra distance
is elo the e te of g a it
e
a suppose that, the
G , at a poi t “ , a d is
D
ep
shown in Figure (1).
From expression (6) we can write
ith si ple pe dulu
The above equation is a quadratic equation i
=
+√
−
−
+
=
D a d it s t o oots a e gi e
=
−√
−
That is for each half of pendulum, there are two different points of oscillation (do not get confusion with
center of oscillation) i.e. which are at
distance away from center of gravity G , for which the
value of L is same. Since L is same for
, then, the time period is also same. When we perform
this e pe i e t o oth sides of e te of g a it G e ha e a total of poi ts poi ts o o e side
ha i g sa e ti e pe iod T , as sho i Figu e . The points
are clearly shown in Graph.
It is so eti es o e ie t to spe if , the lo atio of a is of suspe sio o poi t of os illatio O ,
the
dista e f o e d of the a , i stead of dista e D f o
e te of g a it . B a i g the position of axis
of suspension, measure the corresponding time period, and tabulate all the observation in the following
TABULAR FORM FOR THE DETERMINATION OF TIME PERIOD
S.No
Time period
T=t/20 Sec
Time taken for 20 oscillations
Distance of knife edge
from one end of the bar.
D
Trail 1
Mean time
( t ) sec
Trail 2
1
2
TABULAR FORM FOR THE DETERMINATION OF EQUIVALENT LENGTH OF SIMPLE PENDULUM
+
=
S.No Ti e period T
T2
AC
BD
=
1
2
Graph:
D a a g aph et ee D alues o -a is a d o espo di g T alues o Y- axis, then we get the
follo i g atu e of g aph. Fig . D a a st aight li e, at o e pa ti ula T alue, the it i te se t the
graph at four points and mark them as A,B,C,& D
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1.
alues f o
ta le , o Y-axis, and
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Fig.
T erses D graph for ea h half of the o pou d pe dulu
GRAPH 2.
A g aph is d a
et ee L alues o X-a is a d o espo di g T2
then the nature of graph is as shown in Fig4
NOTE: We a also fi d L alue f o Fig as su
& .
i.e. L=D1 + D2 = PA + PB (According to Fig1)
+
=
+√
−
of
+
. We can show it assum of expression for
−√
−
=
=
PRECAUTIONS: 1.Angular displacement of the pendulum should be confined to below 10 o
2. Pendulum should oscillate only in vertical plane, without wobbling.
3. Knife edge should rest on horizontal surface only.
RESULT:Acceleration due to gravity using compound pendulum was found to be ______.
TORSIONAL PENDULUM-- RIGIDITY MODULUS
AIM: To determine the rigidity modulus of the material of the wire by the method of oscillations.
APPARATUS: Circular disc with chuck, given wire (suspension wire), stop clock, two equal
cylindrical masses, screw gauge, vernier calipers and meter scale.
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FORMULA: Rigidity modulus of given wire using torsional pendulum is given by
−
=
/
−
Here m=mass of each cylinder
= length of the wire
a = radius of the wire
&
�
ℎ
ℎ
&
�
�
�
�
�
�
&
THEORY:
Torsion pendulum consists of a metal wire clamped to a rigid support at one end and carries a heavy circular
disc at the other end. When the suspension wire of the disc is slightly twisted, the disc at the bottom of the
wire executes torsional oscillations such thatthe angular acceleration of the disc is directly proportional to its
angular displacementand the oscillations are simple harmonic.
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PROCEDURE:
One end of a long, uniform wire whose rigidity modulus is to be determined is clamped by a vertical chuck.
To the lower end, a heavy uniform circular disc is attached by another chuck. The length of the suspension
(from top portion of chuck to the clamp) is fixed to a particular value (say 60 cm or 70 cm). Keep the two
cylindrical masses are at equal distance from chuck nut, and note down this distance. At this position, the
suspended disc is slightly twisted so that it executes torsional oscillations. The first few oscillations are
omitted. By using the pointer, (a mark made in the disc) the time taken for l0 complete oscillations are
noted. Two trials are taken. Then the mean time period T (time for one oscillation) is found. The above
procedure is repeated, by keeping the cylinders at various equal distances from chuck nut. The diameter of
the wire is accurately measured at various places along its length with screw gauge. From this, the radius of
the wire is calculated. Tabulate all the observations in the various table forms,
shown below.
TABLE -1 FOR THE DETERMINATION OF RADIUS OF CYLINDER USING VERNIER CALIPERS.
M.S.R
VCxLC
+
S.No
VC
Radius=
cm
a
TABLE-2 FOR THE DETERMINATION OF RADIUS OF CHUCK NUT USING VERNIER CALIPERS
M.S.R
VCxLC
+
S.No
VC
Radius=
cm
a
TABLE-3 FORTHE DETERMINATION OF RADIUS OF WIRE USING SCREW GAUGE
Screw gauge error: ___+ve/___-Ve
Correction ___-ve/___+ve LC=0.001cm
H.S.R
Diameter
P.S.R
b=nxLC
a+
S.No
Corrected
a
cm
Observed
Cm
Radius=
Cm
+
TABLE -4 FOR THE DETERMINATION OF TIME PERIOD OF OSCILLATION
Length of the wire = − − − −
Time
Distance of the
Time taken for 10
period(T)=
cylinder center
oscillations
S.No
t/10 sec
from chuck nut
center (d) cm
Trail-1 Trail-2 Mean(t)
GRAPH: A graph is drawn between
as shown in Figure.
values on Y-axis, then the nature of the graph is
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values on X-axis and
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PRECAUTIONS:
l. The suspension wire should be well clamped, thin long and free from kinks.
2. The period of oscillations should be measured accurately since they occur in second power in the formula.
3. Radius of the wire should be measured very carefully since it occurs in fourth power.
Applications:
1. This method is used to find the moment of inertia of any irregular materials and the elastic limit of the
given wire.
2. By knowing the moment of inertia, the time period of oscillations can be found.
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RESULT: Rigidity modulus of the wire is given by _________dynes/
SONOMETER
AIM: -To verify the laws of transverse vibrations of stretched strings using sonometer.
APPARATUS: -Sonometer set up, Slotted weights 2 ½ kg, Tuning fork box, Rubber pad, paper, Rider, different
types of wires (Brass, Copper and Steel).
PRINCIPLE:- This experiment is based on the principle of resonance, i.e. When a body of known frequency,
excites another body, then the second body vibrates with a different frequency, called frequency of forced
vibration. If frequency of forced vibration matches the frequency of exciting source, then the two bodies are
said to be in resonance.
FORMULA :- The frequency of vibration of a stretched string is given by
of i atio of a stretched string. It is also equal to frequency of exciting tuning fork
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Whe e
= F e ue
at resonance only
√
=
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P = Mode of vibration of a stretched string,
T = Tension applied to the string in dynes.
l = Le gth of i ati g seg e t o it is also alled eso ati g le gth of the i e.
= Li ea de sit of the i e o
ass pe u it le gth of the i e.
DESCRIPTION: - A Sonometer consists of a hollow rectangular box made of teak wood and covered with a
thin plank of soft wood. The box is provided with two long fixed knife-edges parallel to its breadth. At one
end two or three pegs are provided to which the strings of various material and radii can be firmly attached.
These strings may be passed over the fixed knife-edges, carried over tiny smooth pulley at the other end of
the box and attached to weight hangers at their ends. The movable knife-edges can adjust the vibrating
segments of the string. Resonance takes place when the frequency of the external body (tuning fork) is equal
to the natural frequency of the segment of the wire. At resonance energy transfer takes place from the
external body (tuning fork and the segment of wire between A and B vibrates with maximum amplitude. This
can be observed by placing a light weight paper rider at the center of two knife edges (Only in fundamental
mode of vibration or when wire is vibrated in single loop) . At resonance the stretched wire is having
maximum displacement at center of wire, and hence paper rider flies from the wire.
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THEORY: -A stretched string when plucked at its middle and released, it vibrates in a single loop, which is
the fundamental mode of transverse vibrations and emits a ote of f e ue
, depe di g o the te sio
(T) the length of the vibrating loop (l) and the mass per unit length (m) of the wire. The relation connecting
the above quantities is given by:
=
√
−−−−
FIRST LAW:-The frequency of fundamental mode of vibration (P=1) of a stretched string is inversely
proportional to resonating length of the wire , when tension ( T ) and linear density are kept constant. i.e. n x
l =constant
SECOND LAW:-The frequency of fundamental mode of vibration (P=1) of a stretched string is directly
p opo tio al to s ua e oot of the te sio applied,
density are kept constant. i.e.
√
=
he
eso ati g le gth of the
ie
l , a d li ea
It is difficult to verify the second law directly. This is because it is very difficult to p o ide suita le
& T
su h that
is constant. Hence, they are verified indirectly as
√
√
alue
=
THIRD LAW:-The frequency of fundamental mode of vibration of a stretchedstring is inversely proportional
to square root of linear density of the material, when tension and resonating length of wire are kept
=
constant. i.e. √
.
It is diffi ult to e if the thi d la di e tl . This is e ause it is e
su h that
√
PROCEDURE: -
diffi ult to p o ide suita le
is constant. Hence, they are verified indirectly as √
=
alue &
.
(1) Verification of first law: A load is applied to the i e, to p odu e suita le te sio T i it. Pla e a V
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– shaped paper rider at the center of two bridges. Three different tuning forks of known frequency are
chosen and one of them is excited with the help of rubber hammer, and adjust the distance between the two
bridges, till resonance. It should be keet it in mind that the paper rider is always at center of the two bridges.
Measure the distance between two bridges and note it as resonating length of the wire. Keeping the tension
constant (T), measure the resonating length of wire, for each tuning fork frequency.
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(2) Verification of second law: - To verify the second law, the resonant lengths ( ) are determined with
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different tensions (T) using the single fork and sonometer wire.
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(3)Verification of third law: - Measure the resonating length of wire at constant tension and constant
es. Li ear de sit of the ire
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Resonating length of the wire ( l )
Trail 1
Trail 2
nxl = Constant
En
Frequency of
tuning fork (n) Hz
Mean ( l )
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S.No
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T applied = ________X
Constant tensio
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TABLULAR FORM FOR THE VERIFICATION OF FIRST LAW
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(same) tuning fork frequency. Repeat the same on remaining sonometer wires.
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TABLULAR FORM FOR THE VERIFICATION OF SECOND LAW
Linear density of the wire(m) ________
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Constant frequency of tuning fork ( n )___________Hz
Resonating length of the wire ( l )
Tension applied
to
Trail 1
Trail 2
Mean ( l )
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( T ) Dynes
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Graph for first law verification: Plot a graph by taking
�
√
√
=
values on X-a is a d o espo di g l alues o Y-
D
axis, then we get a graph as a straight line passing through origin as shown in Fig.
Graph for second law verification: Plot a graph by taking √ values on X-a is a d o espo di g l alues
on Y- axis, then we get a graph as a straight line passing through origin as shown in Fig.
ll
First law
�
Second law√
PRECAUTIONS : 1.Wire should be free from kinks.
2.Excite the tuning fork with small force by rubber hammer
3.Keep always paper rider only at the center of two knife edges.
RESULT: The laws of transverse vibrations of a string are verified.
NEWTON RINGS
AIM :To determine the radius of curvature of given plano - convex lens by formingNewton rings.
APPARATUS :Plano – convex lens, optically plane glass plate, Plane glass plate inclined at 45 0,sodium
vapour lamp, travelling microscope, reading lens, black sheet.
PRINCIPLE: This experiment is based on the principle of interference.
NATURE OF INTERFERENCE PATTERN:In this experiment all the fringes are circular inshape, with
central dark fringe( in reflected system only). The fringes are circular due tolocus all the points which
are having, constant air film thickness is lie along the circumference of a circle.
FORMULA: The expression for radius of curvature of a given plano-convex lens, in Newton rings
is given by
la
−
−
=
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Here Dm&Dn are the diameters of mth& nth ring respectively.
= Wa ele gth of light sou e used.
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THEORY :
When light from sodium vapour lamp is allowed to fall directly on to a ordinary plane glass plateinclined
at450 , it is reflected at 450 ( according to laws reflection and refraction ) and fall normally (i.e angle of
i ide e i = 0 ) onto the system of plane glass plate and plano-convex lens . When convex surface of
plano- convex lens is placed on plane glass plate, it rest at one point, as shown infig. The airfilm thickness
between convex surface and plane glass plate is gradually increasing fromthe point ofcontact(where
thickness of the film is zero), called wedge shaped film. The light rayswhich fall normallyonto the system
under go first reflection at plano - convex lens surface, andsecond reflection from plane glass plate. Since
both these light rays are derived from same source, they possess same wavelength and has a constant
phase difference equal to thickness of the air filmat that place. These light rays interfere in the field of
view of travelling microscope,producing interference fringes as concentric circles of alternate bright and
dark. This is because, locus of all the points, which are reflecting at same air film thickness lie along the
circumference of a circle.
PROCEDURE:1) Glass plate and lenses are thoroughly cleaned.
2) First one has to detect the plane glass plate and plano-convex lens. This can be done by shaking the lens
while viewing anyobject through it.
(i) If the object is seen through the lens is shaking, when the lens is shaking, then that lens is a plano convex
lens.
(ii) If the object seen through the lensis not shaking, when the lens is shaking, then that one is a plane glass
plate.
Now keep the plano-convex lens on plane glass plate and gently rotate. If it stops rotating immediately, then
it means that the plane side of plano-convex lens is rest on the plane glass plate. If it rotates for some time,
then it means the convex side of plano-convex lens is rest on plane glass plate.
3) The glass plate i the Ne to s i gs appa atus is set su h that it akes a a gle of 0 with the direction
of incident light coming from the source. It is the necessary condition for the well illumination of
combination and to allow light rays to fall normally on to that system.
4) The microscope is moved in the vertical direction till the rings are seen distinctly.
5) The center of the fringes is brought symmetrically below the cross wires by adjusting the position of the
lens and the microscope.
6) The microscope is moved in horizontal direction to one side of the fringes such that one of the cross wires
becomes tangential to the 18th ring. Note down the main and vernier scale readings.
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7) Move the microscope and make the cross wire tangential to the 16th, 14th up to 8th ring and on the other
side up to 18th ring. Note down the readings.
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8) The radius of curvature of the curved surface of the plano-convex lens is determined using spherometer.
Place the lens with its curved surface upwards on the glass plate. Take the spherometer reading when it just
touches the surface. Remove the lens. Take the reading on the plane surface.
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R=
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9) Place the spherometer on the note book and gently press to obtain the impression of the three legs of the
spherometer. Join the three points and determine the mean distance between the legs.
‘adius of ur ature ‘ of pla o-convex surface is given by
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where = distance between two legs of the spherometer, h = thickness of the lens at the centre
TABLULAR FORM FOR THE DETERMINATION OF DIAMETER OF A RING
S.No
Left
Ring
number
VC x LC
Total
reading
RL= a+b
M.S.R
a
Right
VC x LC
Total
reading
RR= a+b
Diameter of
the ring
D = RL~ RR
cm
D2
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M.S.R
a
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Readings of travelling microscope
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GRAPH:
Plot a graph by taking ring number on X- axis and corresponding square of the diameter of the ring on Y- axis,
we get a graph as a straight line passing through origin as shown in Fig. below.
‘ alue a also e fou d f o the g aph, taki g the
slope of the straight line
D2
n
PRECAUTIONS:1) Glass plates and lens should be cleaned thoroughly.
2) In order to avoid any error due to back-lash of the screw in the travelling microscope, the micrometer
screw should be moved only in one direction for the measurement of diameter of rings
3) Crosswire should be focused on a bright ring tangentially.
4) Do the calculation in cgs units only.
RESULT: The radius of curvature of given plano - convex lens was found to be _______ cm
DIFFRACTION GRATING
AIM: -To determine the wavelength of spectral lines of mercury spectrum using diffractiongrating by
normal incidence method.
APPARATUS:-Plane transmission grating, mercury vapor lamp, spectrometer, grating stand,spirit
level, table lamp and magnifying lens.
PRINCIPLE:- Diffraction phenomenon is the principle of this experiment.
FORMULA:- The wavelength of spectral line is given by
=
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He e θ is the a gle of diff a tio
N is u e of uled li es pe e ti ete o g ati g su fa e.
is o de of diff a tio spe t u .
DIAGRAM:
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WORKING:-
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Grating refers to an arrangement of set of parallel lines with equal spacing. The opticalplane
Diffraction grating that we are using consists of a set of parallel lines (15000 lines per inch) drawn on
an optical surface. These ruled lines are opaque to light or acts as obstacle to light propagation, while
the spacesbetween them are transparent. When a monochromatic light of a ele gth is i ide t
normally, thediffracted beams at each ruled line interfere with one another producing diffraction
pattern in thefield of view of telescope. Since we are using mercury vapor lamp (polychromatic) in
this experiment, the diffraction consists of beautiful VIBGYOR on their either sides of the central
maxima. By measuringangle of diffraction, the wavelength of each color can be determined usingthe
above expression.
D
NORMAL INCIDENCE PROCEDURE:Normal incidence means the angle of incidence is zero degrees i.e. we have to set both the light ray
and normal to the surface are parallel to each other, and this can be done as follows by using
spectrometer.
1. Release the locks provided at vernier table and telescope
2. Focus the telescope to a distant object and rotate the Rack& Pinion screw till the image
of the distinct object appears clearly.(NOTE: DO NOT CHANGE THE POSITION OF THE SCREW,TILL THE
EXPERIMENT IS OVER.)
3.Bring the telescope in line with collimator and observe the slit through telescope .If the image of
theslit is blurred, then rotate Rack & Pinion of the collimator till slit appears veryclear.(NOTE:
DO NOT CHANGE THE POSITION OF THE SCREW,TILL THE EXPERIMENT ISOVER.)
4. Coincide the cross wire with slit image and lock the telescope.
5. Set the position of the vernier table at 0° -0° or 0°-180° and lock the vernier table.
6. Release the telescope and rotate it (either left side or right side) through 90° and lockthe telescope.
7. Place the diffraction grating into grating stand and rotate the grating table towards telescope till the
reflected image coincides with the vertical cross-wire. (i.e., angle of incidence is 45°. )
8. Release the vernier table and rotate it through 45° towards collimator and lock it.
9. Release the telescope and observe the diffraction pattern on either side of the central maxima.
MEASUREMENT OF WAVELENGTH:
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After adjusting for normal incidence the telescope is then rotated towards either left or right side of the
central maxima so as to catch first order spectrum. Let us first move the telescope towards left side of the
central maxima. Now set the position of the telescope such that the intersection of cross wires coincides
with red spectral line and note down the reading in any one of the vernier. (It should be noted that all the
readings should be noted from only one vernier i.e., either from vernier-1 or vernier-2. After noting down
the reading, the telescope is move towards next spectral line, and note down the reading of that spectral
line. Repeat the same process for each spectral line on left side of the central maxima.Now the telescope is
moved in the same direction i.e., towards right side of the central maxima such that the cross-wires coincide
with violet to red spectral line. (If you begin your experiment by moving telescope to the right side first, then
the procedure is repeated by noting the spectral line position from right to left side). The difference between
the eadi gs of spe t al li e o left a d ight is e ual to t i e the a gle of diff a tio
θ a d a ele gth of
spe t al li e is dete i ed afte su stituti g θ i the a o e e tio ed fo ula.
sic
� ~� �
�=
Total
reading
RR=a+b
=
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to
fP
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Red
Orange
Yellow
Green
Blue
Violet
VCXLC
Total
reading
RL=a+b
VCXLC
V.C
sM.S.R
,B
aa
pa
V.C tla
En
Readings of the telescope
Left (Degree)
Right (Degree)
M.“.‘ a
Colour of the
spectral line
S.No
gi
n
TABLULAR FORM FOR DETERMINATION OF ANGLE OF DIFFRACTION AND WAVELENGTH:
PRECAUTIONS:
1. Always the grating should be held by the edges. The ruled surface should not be touched.
2. Light from the collimator should be uniformly incident on entire surface of the grating.
RESULT:
The wavelength of all spectral lines of mercury spectrum are calculated and compared with standard
wavelength and found that they are nearly equal.
AIR WEDGE INTERFERENCE
AIM:To determinethe thickness of given hair or wire by forming air wedge interference
APPARATUS:Two optically plane glass plates, sodium vapour lamp, plane glass plate inclined at 45 o,
hair/wire, travelling microscope, black sheet, reading lens.
NATURE OF FRINGE PATTERN:In this experiment the all fringes are in straight in shape, with equal spacing.
This is because locus of all points which are having constant air film thickness is lie along a straight line, and
these fringes are parallel to edge of wedge.
FORMULA: Expression for thickness of given hair/wire is given by
=
cm
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,B
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���� λ= W�����n��� �� ����� ������ ����.
l= Length of air column between the two glass plates
β= F��n�� �����.
RAY DIAGRAM:
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En
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THEORY & PROCEDURE:
Consider two optically plane glass plates and clean well with soft cotton cloth. The wire for which thickness
to be found is inserted between the glass plates at one end. The insertion of wire at one end introduces
varying thickness of air film et ee the glass plates, alled edge shaped fil . The e d of the fil at
which thickness of air film is zero is called edge of the wedge. When light coming from the sodium vapour
lamp is allowed to fall onto a plane glass plate inclined at 45 o, make an angle of incidence 45o, and reflected
with the same angle. These reflected light rays fall in a direction almost along the normal to the set of two
glass plates. i.e. light hit the glass plate at angle equal to zero. Light rays that move towards first glass plate,
get their first reflection from bottom surface of first glass plate, due to change in medium. After reflection
light rays move from air medium towards second glass plate, and get their second reflection from the top
surface of the second glass plate. These two reflected light rays interfere with each other producing
interference fringes. Light rays, which are transmitted through second glass plate, are absorbed by black
sheet kept below the glass plates. The purpose of black sheet is to avoid the interference of light due to
transmitted rays. Optical path difference between the two interfering reflected light rays is given by
ep
ar
� =
µ
+
�
±
D
He e α = a gle et ee the t o glass plates. Additio of te
is due to “to ke s p i iple. “i e light a s
fall normally on to the system i.e. i =0 => r = 0, and µ =1 for air medium, now the above expression becomes
� =
The condition for destructive interference is � =
Therefore� =
±
=
±
=>
=2n ------------(1)
Let be the distance of nth ight f i ge f o
point.
From the above fig =
From expressions 1 and 2
2
=
±
−−−
±
±
edge of edge, a d t
e the thi k ess of ai fil
at that
2
±
=
----------------(3)
Similarly we can write the same for (n+1)th dark fringe, at distance
2
+
+
=
±
=
±
−−−−
Subtracting expression 4 from 3 we get
2 + −
=
 Fringe width =

+
=
−
=
+
−−−−−
From the above it is clear that fri ge idth is i depe de t of
, he e all the f i ges a e e uall spa ed.
Let the gi e i e of thi k ess o dia ete t is at a dista e " from edge of wedge.
=
From the above triangle we can write
=
la
=> =
=>
at
=
T��������
=
ap
From expression (5) we have
,B
=
Since is very small,
=
Readings of telescope
V.C
Cm
Co
lle
V.CxLC
Total
reading
‘= a+
Cm
ee
‘ef
rin
g
M.S.R
a
cm
2
n+4
3
n+8
gi
n
1
Fringe
number
En
S.No
Distance
between four
fringes
A
cm
�
ge
TABLULAR FORM FOR THE DETERMINATION OF FRINGE WIDTH OF FRINGES
�
−
−
−
�
s,
B
Edge of wedge
Hair/Wire
sic
1
2
M.S.R
a
Cm
cm
�
−
−
−
Length of air column
=
−
hy
Position of
telescope
Readings of telescope
V.CxLC
Total reading
V.C
‘= a+
Cm
Cm
=
Distance of each
fringe from
reference fringe
D
Cm
fP
S.No
ap
at
la
TABLE FORM FOR THE DETERMINATION OF LENGTH OF AIR COLUMN
Fringe
width
to
Graph:A graph is drawn between fringe number on x-axis and distance of each fringe from reference fringe
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(D) on Y-axis, and then we get a straight line passing through origin as shown in Figure below. Slope of this
graph gives fringe width.
PRECAUTIONS
1. All the glass plates should be well cleaned before to use them, & handle them only at its edges, such that
no figure prints on glass plates.
2. Readings of travelling microscope should be taken without parallax error.
RESULT : Thickness of the given hire/wire was found to be __________cm
DISPERSIVE POWER OF PRISM
AIM: To determine the dispersive power of a given material of prism
APPARATUS: Prism, Spectrometer, mercury vapour lamp, spirit level and reading lens.
FORMULA: Dispersive power of given material of prism is given by
−
�=
−
Here & are refractive indices of violet and red colour respectively.
µ is the average of the above two refractive indices values.
Refractive index of material of the prism is given by
+
=
ap
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En
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Co
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,B
ap
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He e A = A gle of the p is , Dm = Angle of the minimum deviation
THEORY:
When a ray of white light passes through a prism, it split into constituent colours. The phenomenon of
splitting white light into its constituent colours is called dispersion. The angle through which a white light ray
de iates o passi g th ough a p is of s all ef a ti g a gle A is given by
δ = µ- 1)A.
The angle of deviation depends upon, angle of prism, angle of incidence and material of prism. The variation
of angle of deviation with a gle of i ide e i is as sho i Fig elo .
s,
B
When � increases, δ decreases, reaches a minimum and increases again. For one value of δ, the e a e t o
sic
angles� (angle of incidence) and � (angle of emergence). However at a particular δ = δm , called angle of
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minimum deviation � = � .e. incident ray and emergent ray are symmetrical w.r.t. the refracting faces.
The refracted ray in this case will be parallel to the base. The expression for the refractive index of the prism
µ is gi e
D
Since, ea h olou has its o
i de µ of a ate ial of p is
+
=
−−−−
ha a te isti a ele gth
a d a o di g to Cau h s fo
depe ds o a ele gth as,
=
+
+
ula ef a ti e
+ −−−−−
Where A,B, and C, are constants.
This µ of p is is diffe e t fo diffe e t olou s a d so, f o E
diffe e t a ele gths, de iate th ough
different angles on passing through the prism. This is cause of dispersion.
Since λviolet<λred => µviolet > µred =>δviolet>δred
The another dispersion produced by a prism is the difference in the angles of deviation of two extreme
colours (violet and red) . Actually, this is the angle in which all colours of white light are contained.
If δv&δr a e a gle of de iatio of iolet a d ed olou , the a gula dispe sio = δ v – δr )
Or δv – δr ) = (µviolet - µred) A
Dispersive power of a prism is defined as the ratio of angular dispersion to the mean deviation produced by
the prism. In the dispersed beam, Yellow colour is taken as the mean colour, so mean deviation
δ=
� +�
� =
= (
� –�
�
– )
Thus dispersive power � =
=
(
−
− )
=
−
−
This is expression for dispersive power prism. It depends only on the nature of material of prism.
DESCRIPTION
la
In this experiment, a spectrometer is used to measure angle of deviation of a light ray, when it passes
through a dispersive medium. The spectrometer consists of three main units;
ap
at
(1) Collimator (2)Telescope(3)Prism table.
,B
Collimator:The purpose of collimator is to produce parallel beam of light rays. It consists of two co-axial
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tubes, with an adjustable rectangular slit fixed at one end of the tube, and convex lens is placed at the other
end of the tube. The distance between slit and lens can be adjusted with the help of Rack & Pinion screw.
When the slit is placed at focus of the lens, we get parallel beam of light rays. This can be done by seeing the
slit through telescope, and rotate the Rack &Pinion screw of collimator, such that slit appears clearly. The
collimator is fixed to the instrument and cannot be rotated.
gi
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Prism table:It is a small circular table provided with three leveling screw and is used for keeping the prism
s,
B
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En
on it. The prism table can be raised or lowered and clamped in any position by a screw. By means of another
screw it can be fixed to the vernier table and the two will then turn together. The vernier is provided with a
clamped screw and a tangent screw for fine adjustment. The prism table can be rotated about a vertical axis
passing through its centre.
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Telescope:This is an astronomical telescope whose objective is fitted to the inner end of a hollow tube.
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Exactly fitting into this tube there is another tube which can be moved in or out by Rack &Pinion screw. At
the outer end, the tube ca ies the ‘a sde s e e pie e ith oss i es. The oss i es o sists, ge e all
of the fi e s f o a spide s e , fi ed a oss the tu e o e e ti all a d a othe ho izo tall i f o t of the
eye-piece towards the objective side. The distance of the cross-wires from the eye-piece can be altered by
pushing in or drawing out the eye-piece. The axis of the telescope is perpendicular to the axis of rotation of
the prism table. The telescope can be turned about an axis coinciding with the axis of rotation of the prism
table and can be clamped on any position by the screw . The angle of rotation can be measured, on a circular
scale which is fixed to the telescope and moved along with it. Usually graduated into half degree and the
reading can be noted on two vernier which are fixed diametrically opposite to each other. By means of the
tangent screw the telescope, after it is clamped, can be turned through very small angles and thus fine
adjustments can be made. The telescope is used to receive the parallel beam of light from collimator.
PROCEDURE FOR DETERMINATION OF ANGLE OF PRISM:
The initial adjustments of the spectrometer are made. The given prism is mounted vertically at the centre of
the prism table with its refracting edge facing the collimator. Now the parallel rays of light emerging out
from collimator falls almost equally on the two faces of the prism ABC as shown in fig. The telescope is
turned to catch the reflected image from one face of the prism and fixed in that position. The tangential
screw is adjusted until the vertical cross-wire the fixed edge of the image of the slit. The readings on both the
verniers are noted. Similarly the readings corresponding to the reflected image of the slit on the other face
are also taken. The difference between the two readings of the same vernier gives twice the angle of the
prism. Hence, the a gle of the p is A is dete i ed.
Table form for the determination of angle of prism
S.No
Readings of the telescope
Position of the
telescope
1
2
M.S.R
(a) deg
V.C
Total reading
(a+b) deg
RL
RR
V.C x LC (b)
Left
Right
Angle of the prism
=
~
Deg
DETERMINATION OF ANGLE OF MINIMUM DEVIATION (D):-
s,
B
ap
at
la
En
gi
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ee
rin
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Co
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,B
ap
at
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The vernier table is clamped and the prism table is released. The prism clamped centrally on the prism table
such that the surface of the ground glass is almost parallel to the axis of the collimator and the light from
collimator incident on the polished surface of the prism emerges out from the other polished surface as
shown in fig.
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tm
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sic
The telescope is turned to observe the refracted image of the slit. Looking at the image the prism table is
slowly turned such that the image moves towards the direct position. The telescope is also moved so as to
keep the image of the slit in the field of view. At certain stage it will be found that the image changes its
direction of motion even through the prism is continued to move in the same direction. The position of the
prism is fixed when refracted image of the slit just retraces its path, which is the minimum position of
deviation. The telescope is focused such that the image coincides with the vertical crosswire. The readings of
two verniers are noted. Then prism is removed and the telescope rotated such that the direct image of the
slit coincides with the vertical crosswire. Then the reading of two verniers gives the angle of minimum
deviation of the prism (D). Then refractive index of the prism is found by the formula.
VC LC
V.C
Readings of the telescope at
minimum deviation position
Total
reading
R= a+b
deg
M.S.R(a)
deg
S.No
Colour of the
spectral line
Table form for the measurement of angle of deviation
Direct reading
M.S.R
a
deg
V.C
VCxLC
(b)
Total reading
R=a+bdeg
D=R1-R2
deg
PRECAUTIONS:
1.Do not touch the reflecting surfaces of prism with fingers, after cleaned with soft cloth.
2. Do not disturb all the spectrometer adjustments, till experiment is over.
3. Readings should be taken without parallax error.
RESULT: Dispersive power of material of the prism is given by _______________
=
+
DETERMINATION OF LASER WAVELENGTH BY DIFFRACTION GRATING
AIM: To determine wavelength of LASER source by using plane transmission grating.
APPARATUS: Diode LASER, power supply,, plane transmission diffraction grating, scale, screen, graph
paper.
FORMULA: The condition for nth order diffraction principle maxima is given by
+
=
−−−−−
���� �+� �� ����� �� ���� ���� �� �����n� �����n�, n �� ����� �� ����������n.
=
From Fig 1
√
+
−−−
,
�ℎ
where � � ℎ �
ℎ
The expression for wavelength of LASER source from the above expression is given by
+
]Å
la
√
at
)[
ap
D �� �����n�� ������n �����n� �n� �����n
+
,B
= (
D
FIGURE 1
TABLE FORM
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sic
s,
B
ap
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En
gi
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Co
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THEORY:
We know that grating refers to a set of parallel lines with equal spacing. When such arrangement was
made on a plane glass plate, then it is called optical grating. Each line on the slit is acting as an obstacle
to the light propagation and light undergoes diffraction. The plane transmission diffraction grating used
�n ��� ���������� �� ��n����� �� 5,
��n�� ��� �n��. W���� �� ���� ������ ���� �� � �n� ����� �� ����
���n�����n� ���� �� � . �+� �� ������ �����n� �����n� �� ����� �� ���� ����. W��n LA�ER light falls on
grating surface it is diffracted and diffraction spots were observed on either side of central maxima as
shown in Fig. The distance of each order spot from central bright spot must be equal. At one particular
distance between grating and �����n �����n�� �� ���� D , n��� ���n ��� �����n�� �� ���� ����, �n ����
sides of central maxima. Repeat the same for other distances also.
S.No
Distance between
screen & grating (D)
Distance of nth order from
central maxima
Left
Right
Mean(Xn)
= (
+
)[
√
+
]Å
PRECAUTIONS
1. Clean the grating surface with soft cloth and do not touch thesurface with fingers till the experiment
is over.
2. Mark spots of various orders on graph paper with pencil at the center of that spot.
3. Do not see the LASER light with naked eye, because it cause loss of sensation of vision
RESULT: The wavelength of laser light using plane diffraction grating was found to be_____
CHARACTERISTIC CURVES OF A PHOTO CELL
AIM : To draw the characteristic curves of photo voltaic cell
APPARATUS : photo emissive cell mounted inside a blackened wooden box with a wide slit , Ammeter ,
Lamp and Scale arrangement Power supply for D.C, Anode potential Dry Battery 0-45V, a Rheostat a
plug key, a resistance Box and connecting wires.
PRINCIPLE: This experiment is based on principle of photo electric effect
PHOTO ELECTRIC EFFECT: When a light of suitable frequency falls on some metal surface, electrons are
ejected from that surface, without any delay. This effect is called photoelectric effect and the liberated
electrons are called photo electrons.
FORMULA: The maximum velocity of liberated electrons is given by
=√
���� � =C����� �� �n �������n ,
CIRCUIT DIAGRAM:
/
ap
at
la
En
gi
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ee
rin
g
Co
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ge
,B
ap
at
la
=Stopping potential, m= Mass of electron
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sic
s,
B
THEORY:
We know that according to photoelectric effect, when a light of suitable frequency falls on some
materials called photo sensitive materials like alkali materials, electrons are ejected from that material,
without any time delay. This effect is called photo electric effect and the liberated electrons are called
����� �������n�. T��� ��n �� ������n�� �n ��� ����� �� E�n����n � ������ �� �������. A������n� �� M��
P��n� � ���n��� ������, ����� �n���� ���� ����� ������ �� ������� �n ����� �� �������� ���kets of energy,
having the value integral multiples of h�(Here �is frequency of light). This packet of energy can also
treat as a particle, called PHOTON. Hence showering of light rays onto a material can be treated as
showering of particles or photons coming from light source. These incident photons transfer their
energy, to the outer most electrons of, atoms of photo sensitive material. Some part of energy of photons
is used to liberate the electrons from that metal atom(called work function of that metal), and
remaining energy is given to the same electron in the form of kinetic energy. This can be expressed
mathematically as
=
+
T�� ����� ���������n �� ���� ������ E�n����n � ����� �������� �������n.
is called work function of that
metal. By virtue of their kinetic energy possessed, the liberated photo electrons in photo cell are able to
reach anode and produce some photo current in the circuit, even in the absence of potential difference
applied(i.e at v=0). With the increase of positive potential given to anode, more and more number of
electrons is collected by anode, and there by photo current increases linearly up to some positive
potential and becomes constant at high value of potentials. This is because, at high value of potentials,
all the produced photo electrons at one particular intensity of light, are collected by anode. When
intensity of light source is increased, more photo current is produced in the circuit. When –ve potential
is to anode, because of repulsion, number of photo electrons reaching towards anode decreases and
leads to decrease in photo current with increase of –ve potential, as shown in Fig2. At a particular –ve
potential, photo current in the circuit becomes zero, called STOPPING POTENTIAL. At stopping potential,
the photo electron having maximum kinetic energy is experiencing maximum repulsion from –ve
potential, and hence unable to reach the anode. Due to this photo current is zero in the circuit. Stopping
potential depends up on kinetic energy of photo electron, which intern depends up on photon energy or
frequency of radiation. Hence stopping potential increases with increase of frequency of radiation, and
independent of intensity of radiation.
.
=
=
=√
/
LAWS OF PHOTO ELECTRIC EMISSION
1. There is no time lag between arrival of photon and emission of electron
2. Photo current increases with increase of intensity of radiation and independent of frequency of
radiation
3. Stopping potential increases with increase of frequency of radiation, independent of intensity of
radiation.
PROCEDURE:
Co
lle
ge
,B
ap
at
la
Make the connections as shown in the circuit. Keep the light source at a particular distance say 10 cm
from photo cell. Switch on light source and make the light to incident on photo cell. Note down the
photo current when anode potential is zero. Increase the anode potential in steps of 50 mv and note
down the corresponding photo current, until the current reaches to saturation. Now reverse the
potential applied to photo cell. (i.e anode is now at –ve potential & cathode is at +ve potential). Now
increase the reverse voltage potential in steps of 50 mv till the photo current reaches to zero. Note
down the stopping potential at this intensity. Repeat the same procedure when light source is kept at
20cm away from photo cell.
TABLE FORM
At light intensity I1
ee
Photo current
S.No
REVERSE
Applied potential
mV
Photo current
ap
at
la
En
gi
n
S.No
rin
g
FORWARD
Applied potential
mV
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s,
B
GRAPHS:
Plot the anode potential values on X-axis and anode current valves on Y-axis. We obtain the curves as
shown in the figure. These are known as characteristic curves of a photo voltaic cell.
RESULT: The maximum velocity of photo electron is_______________
SOLAR CELL
AIM: To study the characteristics of a photo voltaic cell ( Solar cell ) and to find Fill factor.
APPARATUS: Solar cell, d.cmilli volt meter, d.c micro ammeter, variable resistance box, 100W Lamp,
connecting wires.
PRINCIPLE: This experiment is based on the principle of photo voltaic effect. i.e. When light energy falls on
to a open circuited P-N junction, electron- hole pairs are created, and they were separated by junction
electric field. These separated charges accumulated on P and N regions and leading to create potential
difference across the ends, called Photo – voltaic effect.
FORMULA: Fill factor of a solar cell is given by
=
Fill Factor =
Where Isc = short circuited current ( when resistance in the circuit is zero i.e. R=0 )
Voc = open circuited voltage ( when resistance in the circuit is infinity i.e. ‘= ∞
is actual maximum obtainable power
at
la
= is the ideal power or dummy power output, and
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g
Co
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ge
,B
ap
The fill factor is defined as the ratio of the actual maximum obtainable power, to the product of the open
circuit voltage and short circuit current. This is a key parameter in evaluating the performance of solar cells.
Typical commercial solar cells have a fill factor > 0.70. Grade B cells have a fill factor usually between 0.4 to
0.7. The fill factor is, besides efficiency, one of the most significant parameters for the energy yield of a
photovoltaic Cells with a high fill factor have a low equivalent series resistance and a high equivalent shunt
resistance, so less of the current produced by light is dissipated in internal losses.
sic
s,
B
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at
la
En
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CIRCUIT DIAMGRAM:
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hy
THEORY:A solar cell (also called photovoltaic cell or photoelectric cell) is a solid state electrical device that
converts the energy of light directly into electricity by the photovoltaic effect. Assemblies of solar cells are
used to make solar modules which are used to capture energy from sunlight. When multiple modules are
assembled together, the resulting integrated group of modules all oriented in one plane is referred to in the
solar industry as a solar panel. The electrical energy generated from solar modules, referred to as solar
power, is an example of solar energy. A solar cell is basically a P-N Junction semiconductor diode, usually
made from silicon. The thickness of P- region and N-region are kept very small so that electrons and holes
generated near the surface can diffuse across the junction before recombination takes place. A heavy doping
of p– and n- regions is recommended to obtain a large photo voltage. When light falls on a pn- junction
diode, photons collide with valence electrons,
and impart them sufficient energy enabling them to leave their parent atom. Thus electron-hole pairs are
generated in both the p- and n- sides of the junction. These electrons and holes reach the depletion region
by diffusion and are then separated by the strong barrier field existing there. However, the minority carrier
electrons in the p-side slide down the potential barrier to reach the n-side, and holes in the n-side move to
the p-side. Their flow continues the minority current, which is directly proportional to the illumination, and
also depends on the surface area being exposed to light. The accumulation of electrons and holes on the two
sides of the junction give rise to an open circuited voltage V oc , which is a function of illumination. The open
circuit voltage for a silicon solar cell is typically 0.6 volt and short circuit current is about 40ma/cm2.
EXPERIMENTAL PROCEDURE
1.Keep the solar cell in the sun light for 15 to 20 minutes.
2. Adjust the rheostat position for resistance so that the volt meter reads zero. This is the short circuit
connection. Note down the value of the current as short circuited current, Isc. Disconnect the rheostat from
circuit, then voltmeter shows maximum reading, note down the value of voltage as open circuit voltage ( V oc
)
3. Increase the resistance by varying the rheostat slowly and note down the readings of current and voltage
till a maximum voltage is read. Ensure to take at least 15–20 readings in this region.
4. Repeat the experiment for another intensity of the illumination source.
5. Tabulate all readings in Table 1. Calculate the power using the relation, P = V xI.
6. Plot I vs. V with Isc on the current axis at the zero volt position and Voc on the voltage axis at the zero
current (see Figure 5.)
7. Identify the maximum power point Pm on each plot. Calculate the series resistance of the solar cell using
the formula as follows : RS = [ DV/DI ].
8. To see the performance of the cell calculate fill factor (FT) of the cell, which can be expressed by the
formula, FF = [ PMax/Isc x Voc ].
at
la
TABLE FORM FOR MEASUREMENT OF POWER
V (Volt)
I (ma)
,B
Ammeter
Power =IxV watt
Co
lle
ge
Volt meter
rin
g
S.No
ap
Reading of volt meter & ammeter
Resistance in
ohms (R)
ee
GRAPH:
gi
n
Draw a graph by taking current values on X-axis and corresponding voltage values on Y-axis, we get the
Isc
ar
ep
PRECAUTIONS:
I(Current)
tm
en
to
fP
hy
sic
V
s,
B
Voc
ap
at
la
En
following nature, as shown in Fig. Also draw two straight lines at V oc and Isc. The area spanned by Isc x Vocis
the dummy power or ideal power produced from the circuit.
D
1. Expose the solar cell to sun light for few minutes, for attaining stable values of current and voltage
2. A resistance in the cell circuit should be introduced so that the current does not exceed the safe operating
limit.
RESULT: The characteristic curve for solar cell was drawn and fill factor was found to be______
FIELD ALONG THE AXIS OF A CUURRENT CARRYING CIRCULAR COIL
AIM : To determine the magnetic field along the axis of a current circular coil, using Stewart-Gees apparatus.
APPARATUS: Stewart-Gees apparatus, D.C. Power supply, magnetometer, commutator,
rheostat, ammeter.
Working formula: The magnitude of the field B along with the axis of a coil is given by
=
/
+
hy
sic
s,
B
ap
at
la
En
gi
n
ee
rin
g
Co
lle
ge
,B
ap
at
la
Where n = number of turns in the coil.
a = radius of the coil
i = current in ampere flowing in the coil
x = distance of the point from the centre of the coil.
µ0 = permeability of free space
In this experiment, the coil is oriented such that, the plane of the coil is along the magnetic meridian. This
can achieved by arranging the plane of the coil parallel to magnetic needle in the magnetometer. When
there was no current through the coil, needle in the magnetometer is rest along geographic north and south
direction (neglecting angle of declination), due ea th s ag eti field. Whe u e t is passi g th ough the
circular coil, magnetic field is produced along the axis of coil i.e along geographic east and west directions.
Now the needle in the magnetometer is under the influence of two magnetic fields,(one is ea th s ag eti
field acting along north to south & the other is magnetic field produced along east-west direction due to
current carrying coil.) acting perpendicular to one another. Due to the influence of above said two fields,
needle in the magnetometer is deflected to an angle � ith espe t to ea th s ag eti field as sho i Fig
shown below. According to tangent law, magnetic field along the axis of circular coil is given by � =
��
�.Usually�� ho izo tal o po e t of ea th s ag etic field (when neglecting angle of declination).
D
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ar
tm
en
to
fP
CIRCUIT DIAGRAM
DESCRIPTION:
The apparatus consists of a circular coil mounted perpendicular to the base as shown in fig. A sliding
compass box is mounted on aluminum rails graded with a scale on the rails, so that the compass is always
slides on the axis of the coil, and distance from the center of the coil can be measured.
PROCEDURE: 1. Place the magnetometer compass box on the sliding bench so that its magnetic needle is at the centre of
the coil. By rotating the whole apparatus in the horizontal plane, set the coil in the magnetic meridian
roughly. In this case the coil, needle and its image all lie in the same vertical plane. Rotate the compass box
till the pointer ends read 0 – 0 on the circular scale.
2. To set the coil exactly in the magnetic meridian set up the electrical connections as shown in Fig. Send the
current in one direction with the help of commutator and note down thedeflection of the needle. Now
reverse the direction of the current and again note down thedeflection. If the deflections are equal then the
coil is in magnetic meridian. Otherwise turnthe apparatus a little, adjust pointer ends to read 0 – 0 till these
deflections become equal.
3. Using rheostat Rh adjust the current such that the deflection is between 50 0 – 600 degrees is produced in
the compass needle placed at the centre of the coil. Read both the ends of the pointer. Reverse the direction
of the current and again read both the ends of the mean deflection at x =0.
4. Now shift the compass needle through 5 cm each time along the axis of the coil and for eachposition note
down the mean deflection. Continue the process till the compass box reaches the end of the bench.
5. Repeat the measurements exactly in the same manner on the otherside of the coil.
6* Keep it mind that same current should flow at all observations. If there is any variation in current due to
fluctuation, adjust the rheostat position to get that same value of current.
TABLE FO‘M FO‘ THE DETE‘MINATION OF B VALUE“.
Tesla
/
)
+
W
=
θ8
(
H
θ5 θ6 θ7
En
θ4
E
θ3
Reverse
8
θ1 θ2
Direct
5
Reverse
W
Direct
West side of the coil
(degrees)
gi
n
θ e=A erage of θ to θ
er
in of θ to θ ) (deg)
θ= A erage
g
Co
lTale θ
ge
B = B Ta θ, Tesla
Ba
pa
tla
East side of the coil
(degrees)
θE=A erage of θ1 to θ4
S.No
Distance of each point from
e ter of the ir ular oil
Deflections in magnetometer
s,
B
ap
at
la
GRAPH: Plot g aph taki g
alo g X-a is, a d ta θ alo g Y- axis, and then we get a bell shaped
graph as shown in Fig. below. The nature of the graph is symmetrical about Y- axis.
sic
PRECAUTIONS: -
fP
hy
1) The coil should be carefully adjusted in the magnetic meridian.
D
ep
ar
tm
en
to
2) All the magnetic materials and current carrying conductors
should be at a considerable distance from the apparatus.
3) The current passed in the coil should be of such a value as to
produce a deflection of nearly 50o -60oWE““T
EA“T
5) Parallax should be removed while reading the position of the pointer. Both ends of the pointer should be
read.
6) The curve should be drawn smooth.
7) The pointer ends should be at zero each time before sending the current through the coil. If they are not
at zero, the top of the glass cover should be gently tapped to bring them to zero.
RESULT:
It was observed that magnetic field along the axis of a circular was found to be decreasing with increase of
distance from center of circular coil. Also the value of magnetic field from above two formula was found be
nearly equal.
PLATINUM RESISTANCE THERMOMETER
AIM :To determine the room temperature using platinum resistance thermometer.
APPARATUS:Platinum resistance thermometer, Callender-Griffiths bridge, mercury thermometer, hot water
bath, sensitive galvanometer, high resistance box, regulated D.C power supply.
PRINCIPLE :This experiment is based on the principle of variation of electrical resistivity of a metal with
temperature.
FORMULA: The formula for unknown temperature using platinum thermometer is given by
=
−
Here St = Resistance of the platinum thermometer at unknown temperature
S0 = Resistance of the platinum thermometer at temperature T = 0 oC.
α = Temperature coefficient of resistance of platinum wire, and it is determined
using the formula
−
−
�/
Here S1& S2 are resistance of the platinum wire at temperatures t1&t2 respectively.
Resistance of the platinum the o ete at a te pe atu e t is gi e
ap
at
St = R ± (0.01x2xBalancing length)
la
=
sic
s,
B
ap
at
la
En
gi
n
ee
rin
g
Co
lle
ge
,B
Here +ve sign is used when balancing length was found on right side of electrical zero, &-ve is used when
balancing length was found on left side of electrical zero.
‘ is known resistance
CIRCUIT DIAGRAM:
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ar
tm
en
to
fP
hy
THEORY:
Resistance thermometers are also called resistive thermal devices (RTD) are the sensors used to
measure temperature by correlating resistance of the RTD element with temperature. We know that
resistance of a metal varies directly proportional to the temperature, and is the basis for resistance
thermometers. Common RTD element is constructed from Platinum, Nickel, Copper, have a unique and
repeatable predictable resistance verses temperature relationship. Invariably most of the resistance
thermometers are made from Platinum wire. This is because
1. Platinum is a noble metal and has the most stable resistance to temperature relationship over largest
temperature range. (i.e. linear relationship between R versus T ).
2.Also R vs T relationship in a highly repeatable manner over a wide temperature range. Whereas other
metals like nickel have limited temperature range i.e. change in resistance per one degree change in
temperature is non linear at temperature above 300oC. Copper has very little temperature range for R
verses T relationship, and it cannot be used above 150 oC because it gets oxidized above that temp.
3.It can be used in the temperature range from -200.0oC to 968oC.
4.Platinum is chemically inert.
Platinum resistance thermometer consists of a fine platinum wire (Platinum coil) wound in a non-inductive
way on a i a f a e M Figu e . The e ds of this i e a e solde ed to poi ts A a d C, f o
hi h t o
thick copper leads run along the length of the glass tube( that closes the set-up)and are connected to
terminals (P1& P2) called platinum leads. Also by the side of these leads, another set of copper leads of same
thickness and length,( which were soldered to the ends of A & C) run along the length of the glass tube and
connected to terminals C1& C2 called compensating leads. The platinum leads and compensating leads are
separated from each other by mica or porcelain separators (D,D).The function of compensated leads to
eliminate the resistance of the connecting leads to platinum wire at all temperatures.
CALLENDE‘ AND G‘IFFITH “ B‘IDGE:
For the measurement of resistance of platinum wire at different temperatures Callender&Griffiths , devised
a odified fo of Wheatsto e idge k o as Calle de & G iffith s idge. This is sho i Figu e . I the
circuit, the ratio of arms P and Q are made equal. The platinum leads are connected to fourth arm S, while
the fi st a ‘ o tai s oils of k o
esista e a ked , , ,….. u its, alo g ith the o pe sati g
leads of the thermometer. Between arms R & S a uniform resistance wire MN of length 2l and resistance
ohm per cm. is connected.
ap
at
la
WORKING FORMULA:
The resistance of the pure platinum wire increases with temperature according to the following relation:
=
+
Where Ro = Resistance of the platinum thermometer at T= 0oC
RT = Resistance of the platinum thermometer at ToC
α = Temperature coefficient of resistance of platinum wire . It is defined as the change in resistance of the
i e pe u it ha ge i te pe atu e. It s u its a e pe deg ee e tig ade. α a be calculated by measuring
the resistance of the platinum resistance thermometer at any twotemperatures T 1& T2 as described below.
ee
−
−
gi
n
=> � =
rin
g
Co
lle
ge
,B
Let R1& R2 be the resistance of the platinum thermometer at temperatures T 1& T2 respectively, then
=
+
=
+
+
=>
=
+
=>
+
=
+
ap
at
la
s,
B
PROCEDURE:
1.Determination of electrical zero:
En
Determination of resistance of platinum thermometer at any temperature, was clearly shown under 3 rd point
of procedure mentioned below.
to
fP
hy
sic
Complete the connections as shown in Fig.1. Shot circuit the gaps PL and CL, i.e. connect the above terminals
by thick copper wire. Make the resistance R zero by moving the key of variable resistance. Determine the
position of null point by moving the jockey on the bridge wire MN. The null point gives the position of
electrical zero. This should be note down.
tm
en
2.Determination of resistance per unit length of the bridge wire:
D
ep
ar
To dete i e the alue of
the gaps PP a d CC a e sho t i uited. The alue of “ is adjusted to s all
alue ‘ to o tai the ala e. Let the ala e e o the left side of ze o at a dista e
f o the
position of electrical zero.
0 =
−
=> = /
3.Determination of resistance of platinum thermometer at any temperature:
Connect the platinum leads and compensating leads of platinum thermometer to the Callender&G iffith s
bridge at PL & CL respectively. Other connections are made as per circuit diagram as shown in Figure 1. Place
the bulb of the thermometer in a ordinary water bath at room temperature, and wait for some time to
ensure that it has acquired the temperature of water. Note the temperature of water bath with help of
mercury thermometer. By introducing suitable resistance in the circuit of compensating leads with help of
a ia le esista e ‘ su h that the gal a o ete sho s opposite defle tio s, he jo ke as pressed at
the extreme ends of the bridge wire. Press the jockey at various points on the bridge wire MN such that
gal a o ete sho s ull defle tio let at poi t D f o ze o . Let
be the distance of null point found on
left side from electrical ze o. The le gth of the i e elo gs to ‘ a is
= − ,whereas length of
i e elo gs to “ a is
= + .
The resistance of wire of length MD is −
Resistance of wire of length DN is
+
.
Therefore total resistance in first arm is
Therefore total resistance in fourth arm is
+ +
+ +
−
+
he e
.
is esista e of o pe sated leads
Since P & Q were already made equal, when bridge is balanced resistance in third and fourth arm should be
equal.
i.e + + −
= + + +
+ +
−
=
+ +
+
= –
If the balancing length was found on right side of electrical zero, then the above expression changes to
=
+
Therefore resistance of platinum thermomete at a te pe atu e T = t is gi e
=
±
Repeat the same at various temperatures and enter observation into the observation table (shown below)
for calculation of the resistance at those temperatures.
Co
lle
ge
,B
ap
at
la
TABLE FORM FOR THE DETERMINATION RASISTANCE OF PLATINUM THERMOMETER
Temperature
Known
Balancing length
St = R + (2 x 0.01 x Balancing
of the water
resistance
S.No
length)
Left (-ve)
Right(+ve)
bath (ToC)
‘ �"
1
ep
ar
tm
en
to
fP
hy
sic
s,
B
ap
at
la
En
gi
n
ee
rin
g
DEMERITS.
1.It takes long time to read temperature of a body, as wire may not attain the temperature of the bath in a
short time.
2.With this thermometer changing temperature cannot be measured.
3.It can be used only when the body is of bigger size, and cannot be used to measure temperature at a point.
GRAPH:
From the above observation plot a graph by taking temperature values on x-axis and resistance of platinum
thermometer on Y-axis, then we get a straight line with positive slope as shown in Figure. Extrapolate the
graph on to Y- axis, then the intercept gives value of Ro
D
PRECAUTIONS:
1. Do not allow large value of current through the circuit, otherwise galvanometer may burn.
2. Check all connections are in tight position or not.
3. Note down the temperature of water bath against the null deflection observed in circuit.
RESULT: ‘oo
te pe atu e as dete
i ed f o
plati u
the
o ete a d it s alue is_
DETERMINATION OF ENERGY GAP OF A SEMICONDUCTOR
AIM: To determine energy gap of a semiconductor.
APPARATUS: P-N diode, DC regulated power supply, Voltmeter, Milli ammeter, 1 KW resistor, Beaker,
Thermometer, Heater.
PRINCIPLE: Semiconductor energy gap is determined by passing small forward current
through Si, Ge, GaAsAl, GaAsP, SiC junction diodes. The junction voltage variation is studied with
temperature. From temperature versus junction voltage curve, energy gap is determined.
FORMULA: A pn crystal is called junction diode. Diode can be forward or reverse biased using a voltage
source. During forward bias forward current flows through the diode. The forward current is given by
=
− ]
IF is called forward current
IR is called reverse current or reverse saturation current
q is electronic charge e =1.6x10-19 Coulomb
η is alled idealit fa to a ies et ee a d . [ ]
k is Boltzman constant = 1.38x10-23J/K
T is temperature in degree Kelvin.
When the diode is reverse biased negligible reverse current flows through the diode. The reverse current is
given by
−
(
⁄
)
rin
g
=
Co
lle
ge
,B
ap
at
la
Where
⁄
[
{
−
ap
at
la
⁄
s,
B
=
En
gi
n
ee
The constant B appearing in equation 2 is a constant connected with the structure or the area of the
depletion region.
Substituting equation 2 in equation 1, we get
⁄
=
{
}{
⁄
⁄
− }
− }
ar
tm
en
to
fP
hy
sic
Taking natural logarithm on both sides, we get the following expression for junction voltage verses
temperature.
=
=
+
−[
]
D
ep
The above Eq represents a straight line, and its slope, Y- intercept are given by
=−
[
]
=
Energy gap EG is determined from Y-intercept at T= 0K i.e
EG = q Yintercept in Joules.
We know that 1eV= 1.6x10-19 Joules. ⇒ J���� =
.6�
−19
∴ EG = q Yintercept {
Circuit diagram
.6�
−19
} eV
⇒ EG = Yintercept in eV (since q =1.6x10-19 Coulomb)
at
la
THEORY:
In an atom electron occupy distinct energy levels. When atoms join to make a solid, the allowed energy
levels are grouped into bands. The bands are separated by regions of energy levels that the electrons are
forbidden to be in. These regions are called forbidden Energy gaps or band gaps. Energy bands and the
forbidden energy gap is illustrated in figure 1. The electrons of the outermost shell of an atom are the
valence electrons. These occupy the valence band. Any electrons in the conduction band are not attached
to any single atom, but are free to move through the material when driven by an external electric field.
D
ep
ar
tm
en
to
fP
hy
sic
s,
B
ap
at
la
En
gi
n
ee
rin
g
Co
lle
ge
,B
ap
In a metal such as copper, the valence and conduction bands overlap as illustrated in figure 2a. There is no
forbidden energy gap and electrons in the topmost levels are free to absorb energy and move to higher
energy levels within the conduction band. Thus the electrons are free to move under the influence of an
electric field and conduction is possible. These materials are referred to as conductors. In an insulator such
as silicon dioxide (SiO2), the conduction band is separated from the valence band by a large energy gap of 9.0
eV. All energy levels in the valance band are occupied and all the energy levels in the conduction band are
empty. It would take 9.0 eV to move an electron from the valence band to the conduction band and small
electric fields would not be sufficient to provide the energy, so SiO 2 does not conduct electrons and is called
an insulator. Notice the large energy gap shown in figure 2b. Semiconductors are similar to the insulators
insofar as they do have an energy gap only the energy gap for a semiconductor is much smaller ex. Silicon's
energy gap is 1.1 eV and Germanium's energy gap is 0.7 eV at 300 °K. These are pure intrinsic
semiconductors. Observe the energy gap in figure 2 c.
For finite temperatures, a probability exists that electrons from the top of the valence band in an intrinsic
semiconductor will be thermally excited across the energy gap into the conduction band. The vacant spaces
left by the electrons which have left the valence band are called holes which also contribute to the
conduction because electrons can easily move into the vacancies. If an electric field is applied, the electrons
flow in one direction and the holes move in the opposite direction. The holes act as a positive charge
(deficiency of negative charge) so the direction of current (effective positive charge) is in the same
direction. For pure silicon at 300 °K, the number of electrons residing in the conduction band as a result of
thermal excitement from the valence band is 1.4 x 1010 /cm3.
At absolute zero degree temperature, semiconductors are pure insulators. As the temperature is increased
thermal energy create vibrations in crystal lattice and few electrons, which acquire sufficient vibrational
En
gi
n
ee
rin
g
Co
lle
ge
,B
ap
at
la
energy break their covalent bond, become free, and move to the conduction band. The energy required to
rapture the covalent bond is designated as energy gap E G and termed as energy gap or band gap energy.
Energy less than EG is not acceptable or one cannot have partially ruptured bond, hence this energy is also
called as forbidden gap energy. In silicon crystal, at room temperature (300ºK) about 10 19 covalent bonds are
broken per cubic meter out of 1029 atoms. It is only one atom in 1010 exits with broken bond. This is less than
one atom per thousand atoms on each of the three-crystal axis. The electrons that are freed take part in
conduction and the material becomes semiconductor. Such a semiconductor is known as intrinsic
semiconductor. The resistivity of such a semiconductor falls in the range of 0.4 to 2500 ohmmeter. As the
temperature increases above room temperature more and more covalent bonds are broken and conduction
increase rapidly and resistivity fall. Intrinsic semiconductors are useless for electronics applications because
of their low conduction at room temperature. Adding impurity atom from the third or fifth group elements
can increase the conduction. This process of adding impure atom is known as doping and the doped
semiconductor becomes extrinsic semiconductor. Addition of impurity from the fifth group element result in
n-type semiconductor and addition of impurity atom from third group results in p-type semiconductor.
Energy gap is a very important parameter of semiconductor that decides its applicability. Determination of
semiconductor energy gap is an important experiment in physics lab. Pure semiconductors or intrinsic
semiconductors are not available easily for measurements. Extrinsic semiconductors are easily available for
EG measurements.
PROCEDURE:
To determine the energy gap EG a small constant current of the order of 100 –
A is passed th ough the
diode at various temperatures. The voltages developed at the junction are noted. The junction voltage versus
temperature graph is drawn. From the straight-line graph, Y intercept gives the EG directly in electron volt.
From the slope, constant B is calculated using equation. For small forward current of the order of hundreds
of microampere e slope is unity. Which indicate that the graphs for different diodes are all parallel and the
constant B is independent of diode material, it depends only on the forward current, hence it is connected
with majority carriers.
Temp.of the bath
(Centigrade)
Temp.of the bath (Kelvin)
Junction voltage (mV)
sic
S.No
s,
B
ap
at
la
TABLE FORM FOR THE MEASUREMENT OF JUNCTION VOLTAGE
Constant current passing through the semiconductor/diode is_____________
tm
en
to
fP
hy
1
2
D
ep
ar
GRAPH:
A graph is drawn between temperature of the bath on X-axis and corresponding junction voltage values on
Y-axis we get a straight line as shown in Fig. below.
RESULT: Energy gap of given semiconductor diode is ____________
HALL EFFECT
Aim: To determine the hall coefficient (kH), mobility of charge carriers(µ) and concentration of charge
carriers(n) in a given material
Apparatus: Hall probe, Hall effect setup for measurement of current and voltage, electro-magnet, constant
dc power supply to electro-magnet and Gauss meter.
,B
ap
at
la
Hall Effect: When magnetic field is applied perpendicular to a current carrying conductor, then a voltage is
developed in a direction both perpendicular to charge flow and applied magnetic field direction ; is known as
Hall effect. The developed voltage is known as Hall voltage(vH).
ee
,
En
gi
n
&
=
=
.
=
−
.
hy
sic
s,
B
���� =
=
=
ap
at
la
�−
rin
g
=
Whe e e is the ha ge of ele t o ,
=
Co
lle
ge
CIRCUIT DIAGRAM
FORMULA:
ar
= ��� −
ep
=
D
=
tm
en
to
fP
Mobility of charge carriers (µ)= KH σ
here σ = o du ti it of sa ple = /ρ
ρ= resisti it of sa ple, gi e
=
" "=
=
THEORY:
Let us consider a rectangular plate of a conductor or semiconductor placed with its thickness along zdirection, the length along the x-direction and width along y-direction as shown in the above Figure1. Let a
voltage be applied along x-direction such that it produce a current Ix, given
by =
ℎ
�
� & �
�
.Now let a magnetic field
is
applied along Z-direction. The applied magnetic field deflects the charge carriers towards positive Ydi e tio , a d di e tio of defle tio fo e a e k o
f o Fle i g s left ha d ule. If the gi e sa ple
contain both +ve and –ve charges, then both of them will be deflected towards same side, leading to
creation of potential difference between top and bottom face of the sample(i.e. along Y-direction), called
hall voltage. After creation of potential difference charged particles moving along x- direction do not under
go any deviation from magnetic field, and move in straight path. This is because the deflection force from
magnetic field is balanced by force exerted by Hall electric field (i.e., force of repulsion exerted by already
settled charges on the top surface of the sample).
At equilibrium the above two mentioned forces are equal.
=>
=
.
=
=
(
)
=
(
)
=
The term is is called Hall coefficient denoted by RH. It is numerically equal to the developed Hall electric
field when unit strength current is passing through the sample, in the presence of unit strength of externally
applied magnetic field.
We kno that the elatio et ee E, V a d d is E = V/d
=>
=>
=>
=
[
[
=
=
=
= ]
]
=
From the above expression we can calculate density of charged carriers.
We k o that o du ti it of the sa ple σ = eµ
Where µ is mobility of charged carrier. It is defined as the drift velocity acquired by charged carrier under the
application of unit electric field.
�
la
=> µ =
En
gi
n
ee
rin
g
Co
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ge
,B
ap
at
=>µ = �� �
PRACTICAL:
In the experiment Hall probe consists of a semiconductor sample in square shape having four pressure
contacts as shown in fig. The two opposite ends are connected by a same color wire.
to
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s,
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1.For the measurement of resistivity of sample connect one red and one green wire to current terminals,
and other two wires connected to voltage terminals of Hall effect setup. Measure the voltage (V x) for each
current value and tabulate them.
2.Connect one set of same colour wires to current terminals and other set of colour wires to voltage
terminals of Hall effect setup. Measure the error voltage (i.e., voltage in the absence of magnetic field) at
different values of current passing through the sample. Measure the transverse voltage or Hall voltage in the
presence of magnetic field for the same values of current passing through the sample, for the measurement
of error voltage. The difference in the two voltages is the correct Hall voltage.
tm
en
Table – I:FOR THE MEASUREMENT OF RESISTIVITY
Current
Ix (mA)
Voltage
Vx (mV)
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S.No.
Table – II: FOR THE MEASUREMENT OF HALL VOLTAGE.
Transverse voltage(OR)HALL VOLTAGE
S.No. Current
Ix
With out
magnetic field
a
With
magnetic field
True Transversevoltage
(OR)
True Hall voltage
Vy= b-a
(mv)
Model graph:
(1) Plot the graph between Ix on x-axis, Vx on y-axis, we get a straight line.
(2) Plot the graph between Ix on x-axis, VH on y-axis we get a straight line.
Vx
IxIx
CALCULATION PART:
(1).Find the slope of straight line in the graph (i.e., IxVsVx) and it is equal to resistance
( R ) of the sample.
(2). We know that Resistivity
(3).Conductivity � =
Ω−
(4). Find the slope of
−
[
= ]Ω−
expression.
µ =
�
,B
ap
at
la
Ω-m3/Web
)=
/
ge
.
(7).
=
graph, put this value in
=
=
=
−
Co
lle
(5).
=
��n�� � � =
�
ee
rin
g
Sample dimensions are l = b = 5mm = 5X10-3m, t =0.5mm = 0.5X10-3m
gi
n
PRECAUTIONS:
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En
1 Increase slowly the current through electromagnet from power supply (max up to 2A).
2 Before to switch off power supply, reduce current to zero and the switch off.
sic
s,
B
3 Keep the probe in the Gauss meter at the center of pole pieces and rotate at till it shows maximum reading
for the measurement of magnetic field.
ep
D
3.
4.
fP
−−−−−−−Ω−
to
=
ar
2.
−
tm
en
1.
hy
RESULT:
� =
µ =
/��
−−−−−−Ω−
−
−−−−−−−−
�=−−−−−−
/
−
CATHODE RAY OSCILLOSCOPE
AIM:- To study the different waveforms, to measure peak and rms voltages and thefrequency of A.C.
APPARATUS:- A C.R.O and a signal generator.
BLOCK DIAGRAM OF CRO: The various main parts of CRO are shown in Fig. below
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THEORY :Cathode ray oscilloscope is one of the most useful electronic equipment, which gives a visual representation
of electrical quantities, such as voltage and current waveforms in an electrical circuit. It utilizes the
properties of cathode rays of being deflected by an electric and magnetic fields and of producing
scintillations on a fluorescent screen. Since the inertia of cathode rays is very small, they are able to follow
the alterations of very high frequency fields and thus electron beam serves as a practically inertia less
pointer. When a varying potential difference is established across two plates between which the beam is
passing, it is deflected and moves in accordance with the variation of potential difference. When this
electron beam impinges upon a fluorescent screen, a bright luminous spot is produced there which shows
and follows faithfully the variation of potential difference. When an AC voltage is applied to Y-plates, the
spot of light moves on the screen vertically up and down in straight line. This line does not reveal the nature
of applied voltage waveform. Thus to obtain the actual waveform, a time-base circuit is necessary. A timebase circuit is a circuit which generates a saw-tooth waveform. It causes the spot to move in the horizontal
and vertical direction linearly with time. When the vertical motion of the spot produced by the Y-plates due
to alternating voltage, is superimposed over the horizontal sweep produced by X-plates, the actual
waveform is traced on the screen.
PROCEDURE:STUDY OF WAVEFORMS:
To study the waveforms of an A.C voltage, it is ledto the y – plates and the time base voltage is given to the
X-plates. The size of the figure displayed on the screen, can be adjusted suitably by adjusting the gain
controls. The time base frequency can be changed, so as to accommodate one, two or more cycles of the
signal. There is a provision in C.R.O to obtain a sine wave or a square wave or a triangular wave.
MEASUREMENT OF D.C.VOLTAGE : Deflection on a CRO screen is directly proportional to the voltage applied to the deflecting plates. Therefore,
if the screen is first calibrated in terms of known voltage.i.e. the deflection sensitivity is determined , the
direct voltage can be measured by applying it between a pair of deflecting plates. The amount of deflection
so produced multiplied by the deflection sensitivity, gives the value of direct voltage.
MEASUREMENT OF A.C VOLTAGE : To measure the alternating voltage of sinusoidal waveform, The A.C. signal, from the signal generator, is
applied across the y – plates. The voltage(deflection) sensitivity band switch (Y-plates) and time base band
switch (X-plates) are adjusted such that a steady picture of the waveform is obtained on the screen. The
vertical height (l) i.e. peak-to-peak height is measured. When this peak-to-peak height (l) is multiplied by the
voltage(deflection) sensitivity (n) i.e. volt/div, we get the peak-to-peak voltage (2Vo). From this we get the
peak voltage (Vo). The rms voltage Vrms is equal to Vo/ 2 . This rms voltage Vrms is verified with rms voltage
value, measured by the multi-meter.
TABLE-1 FOR VOLTAGE COMPARISION
Height of the
Applied
signal (or)
voltage
S.No
Number of
A Volts
di isio s
Observed
voltage
B = xy Volts
Volt/Div
(y)
difference in
volts
A~B Volt
ee
gi
n
Time period
T = xy sec.
Observed
frequency
B = 1/T
Difference in
frequency
A~B Hz
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En
TABLE -2 FOR FREQUENCY COMPARISION:
Applied
Width of the
Time/Div
S.No
frequency
sig al
A Hz
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MEASUREMENT OF FREQUENCY : An unknown frequency source (signal generator) is connected to y- plates of C.R.O . Time base signal is
connected to x – plates (internally connected) . We get a sinusoidal wave on the screen, after the adjustment
of voltage sensitivity band switch (Y-plates) and time base band switch (X-plates). The horizontal length(l)
between two successive peaks is noted. When this horizontal length (l) is multiplied by the time base(m) i.e.
sec/div , we get the time-period(T).The reciprocal of the time-period(1/T) gives the frequency(f). This can be
verified with the frequency, measured by the multi-meter.
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B
PRECAUTIONS :1) The continuity of the connecting wires should be tested first.
2) The frequency of the signal generator should be varied such that steady wave form isformed.
3. An oscilloscope should be handled gently to protect its fragile ( and expensive) vacuum tube.
4. Oscilloscopes use high voltages to create the electron beam and these remain for some time after switchoff. For your own safety do not attempt to examine the inside of an oscilloscope.
D
ep
ar
RESULTS : - The voltage, and frequency of given ac signal were measured & compared, and they were found
nearly equal.
RESONANCE IN LCR CIRCUIT
ap
at
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En
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rin
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Co
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,B
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AIM: To study resonance effect in series LCR circuit and quality factor.
APPARATUS: A signal generator, inductor, capacitor, ammeter, resistors, AC milli voltmeter.
BASIC METHODOLOGY:
In the series LCR circuit, an inductor (L), capacitor (C) and resistance(R) are connected in series
with a variable frequency sinusoidal emf source and the voltage across the resistance is measured. As
the frequency is varied, the current in the circuit (and hence the voltage across R) becomes maximum at
1
the resonance frequency f r 
. In the parallel LCR circuit there is a minimum of the current at
2 LC
the resonance frequency.
THEORY:Circuits containing an inductor L, a capacitor C, and a resistor R, have special characteristics useful in
many applications. Their frequency characteristics (impedance, voltage, or current vs. frequency) have
a sharp maximum or minimum at certain frequencies. These circuits can hence be used for selecting or
rejecting specific frequencies and are also called tuning circuits. These circuits are therefore very
important in the operation of television receivers, radio receivers, and transmitters. In this section, we
will present two types of LCR circuits, viz., series and parallel, and also discuss the formulae applicable
for typical resonant circuits. A series LCR circuit includes a series combination of an inductor, resistor
and capacitor whereas; a parallel LCR circuit contains a parallel combination of inductor and capacitor
with the resistance placed in series with the inductor. Both series and parallel resonant circuits may be
found in radio receivers and transmitters.
SERIES RESONANCE CIRCUIT:-
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s,
B
When an alternating e.m.f� = � � � 0 was applied to circuit having an inductance L,capacitance C
and resistance R in series as shown in fig. The current in the circuit atany instant of time t isgiven by the
following equation
� =� � � −�
Where it can also be proved that the maximum current � is
tm
en
=
√� + � −
�
−−−−−
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From the above expression(1)the impedance of circuit is given by is
= √� + (� −
�
)
The L - C - R series circuit has a very large capacitive reactance (� ) at low frequencies and a very large
inductance reactance (� ) at high frequencies. So at a particular frequency, the total reactance in the
circuit is zero (� = � . Under this situation, the resultant impedance of the circuit is minimum. The
particular frequency of A.C at which impedance of a series L - C - R circuit becomes minimum is called
the resonant frequency and the circuit is called as series resonant circuit.
� =
At resonance frequency
=>
�
=> � =
=
√
√
�=
The above equation shows that the resonant frequency depends on the product of L and C and does not
depend on R. The variation of the peak value of current with the frequency of the applied e.m.f is shown in
Fig.
Let f1 and f2 be these limiting values of frequency. Then the width of the band is
� = −
The quality factor is defined as
=
=
−
Q-factor is also defined in terms of reactance and resistance of the circuit at resonance,
�
=
ap
at
la
En
gi
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Co
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,B
ap
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PROCEDURE:
1. The series and parallel LCR circuits are to be connected as shown in fig 1 & fig 2.
2. Set the inductance of the variable inductance value and the capacitances the variable capacitor to low
1
is of order of a few kHz .
values ( L ~ 0.01H , C ~ 0.1 µ F ) so that the resonant frequency f r 
2 LC
3. Choose the scale of the AC milli voltmeter so that the expected resonance occurs at approximately the
middle of the scale.
4. Vary the frequency of the oscillator and record the voltage across the resistor.
5. Repeat (for both series and parallel LCR circuits) fir three values of the resistor (say R = 100, 200
&300 ).
TABLE FORM
L = _______________________ mH C = _______________________ µF.
Voltage across resistor (R)
Applied frequency
S.No
f Hz
R=
R=
R=
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en
to
fP
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s,
B
RESULT :
Estimated value of Q for series resonance from graph :
Resonance frequency for series LCR circuit =________________kHz
COMPOUND PENDULUM
AIM : To determine acceleration due to gravity ( g )at a place using compound pendulum.
APPARATUS: Compound pendulum, knife edges, telescope, stop watch, meter scale.
DEFINATION OF g : When a body is left to free fall, then it acquires a constant acceleration and move
to a ds ea th, due to ea th s g a itatio . No the o sta t a ele atio acquired by that freely falling body
is called acceleration due to gravity.
FORMULA: Time period of oscillation of a physical pendulum or compound pendulum is given by
=
√
+
Compare the above formula with time period of oscillation of a simple pendulum. i.e.
is alled le gth of e ui ale t si ple pe dulu . K is adius of g atio ; D is dista e of the
�
et ee
cm/s2
ge
From the above formula acceleration due to gravity is given by � =
a g aph d a
,B
point of suspension from center of gravity. The value of L is esti ated f o
distance of point of suspension ( ) verses time period of oscillation (T)
la
+
at
= √
ap
Here
√
=
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to
fP
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s,
B
ap
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En
gi
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Co
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THEORY:
In lower classes you might be familiar with simple pendulum experiment for the determination of
acceleration due to gravity, hence before to do this experiment one has to know the difference between
simple pendulum, and compound pendulum experiment, both of them were meant for determinatio of g
value. They are
3. Simple pendulum is an ideal case, because it require a point mass object
4. It requires torsion less string.
The above mentioned two conditions are not practically possible, hence it is only a mathematical ideal case,
and whereas compound pendulum is a physical pendulum.
A rigid body of any shape which is free to oscillate without any friction on a vertical plane is called
compound pendulum. It swings harmonically back and forth about a vertical z-axis (Passing through
point O as shown in Fig),when compound pendulum is displaced from its equilibrium position by an
angle . In the equilibrium position, the center of gravity of the body is vertically below at a distance
of OG. Let the mass of the body is m, In this experiment you are going to measure the acceleration
due to gravity, g by observing the motion of a compound pendulum. Let us consider a compound
pendulum shown in figure 1.
Pull the compound pendulum through an angle
torque acting on it, given by
and release it, then it makes angular oscillations due to
⃗⃗� = ⃗ ⃗
⃗ = ⃗⃗⃗⃗⃗⃗ ⃗⃗⃗⃗⃗⃗⃗⃗
�
�
⃗ =−
−−−−−−−−
Here –ve sign is because of force and displacement are opposite to each other.
For small amplitudes
≈
Now expression (1) becomes ⃗⃗� = −
We know that torque �
⃗⃗ =
� =
=−
=>
+(
[
)
]
=
−−−−
Here is the o e t of i e tia of pe dulu , a out a a is passi g th ough poi t O .
Equation (2) represents simple harmonic equation of the form, i.e.
+�
=
Here �is angular frequency of simple pendulum. From comparison with Eq (2), we can write
�= √
=√
=>� =
=> =
−−−−
√
+
√
=
+
−−−−−
ee
√
=
gi
n
Thus
rin
g
Co
lle
ge
,B
ap
at
la
According to parallel axes theorem, the rotational moment of inertia, about any axis parallel to the one
passing the center of gravity is given by
=
+
−−−
We know that moment of inertia a out a a is passi g th ough e te of g a it G , gi e
=
He e K is adius of g atio of the od a out a a is passi g th ough G .
=
+
√
=
+
ap
at
la
This suggests that
=
En
Comparing expression (5) with expression for time period of simple pendulum i.e.
−−−−
=
fP
hy
sic
s,
B
The term L is called length of equivale t si ple pe dulu .
This is e ause si ple pe dulu of le gth L is ha i g a ti e pe iod, sa e as that of ti e pe iod of
compound pendulum. Also it seems that all the mass of the body were concentrated at point “ , along
to
OG p odu ed su h that
=
+
=
+
=
ar
tm
en
The poi t “ is alled e te of os illatio . I a alog
entire mass is concentrated at that point.
ep
From expression (6), the extra distance
D
shown in Figure (1).
From expression (6) we can write
The above equation is a quadratic equation i
=
+√
−
ith si ple pe dulu
is elo the e te of g a it
e
a suppose that, the
G , at a poi t “ , a d is
−
+
=
D a d it s t o oots a e gi e
=
−√
−
That is for each half of pendulum, there are two different points of oscillation (do not get confusion with
center of oscillation) i.e. which are at
distance away from center of gravity G , for which the
value of L is same. Since L is same for
, then, the time period is also same. When we perform
this e pe i e t o oth sides of e te of g a it G e ha e a total of poi ts poi ts o o e side
having same time pe iod T , as sho i Figu e . The poi ts
are clearly shown in Graph.
It is so eti es o e ie t to spe if , the lo atio of a is of suspe sio o poi t of os illatio O ,
the
dista e f o e d of the a , i stead of dista e D f om center of gravity. By varying the position of axis
of suspension, measure the corresponding time period, and tabulate all the observation in the following
TABULAR FORM FOR THE DETERMINATION OF TIME PERIOD
S.No
Time period
T=t/20 Sec
Time taken for 20 oscillations
Distance of knife edge
from one end of the bar.
D
Trail 1
Mean time
( t ) sec
Trail 2
1
2
TABULAR FORM FOR THE DETERMINATION OF EQUIVALENT LENGTH OF SIMPLE PENDULUM
+
=
S.No Ti e period T
T2
AC
BD
=
1
2
Graph:
D a a g aph et ee D alues o -a is a d o espo di g T alues o Y- axis, then we get the
follo i g atu e of g aph. Fig . D a a st aight li e, at o e pa ti ula T alue, the it i te se t the
graph at four points and mark them as A,B,C,& D
s,
B
ap
at
la
En
gi
n
ee
rin
g
Co
lle
ge
,B
ap
at
la
2.
alues f o
ta le , o Y-axis, and
D
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to
fP
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sic
Fig.
T erses D graph for ea h half of the o pou d pe dulu
GRAPH 2.
A g aph is d a
et ee L alues o X-a is a d o espo di g T2
then the nature of graph is as shown in Fig4
NOTE: We a also fi d L alue f o Fig as su
& .
i.e. L=D1 + D2 = PA + PB (According to Fig1)
+
=
+√
−
of
+
. We can show it assum of expression for
−√
−
=
=
PRECAUTIONS: 1.Angular displacement of the pendulum should be confined to below 10 o
2. Pendulum should oscillate only in vertical plane, without wobbling.
3. Knife edge should rest on horizontal surface only.
RESULT. Acceleration due to gravity using compound pendulum was found to be ______.
NEWTON RINGS
AIM :To determine the radius of curvature of given plano - convex lens by forming Newton rings.
APPARATUS : Plano – convex lens, optically plane glass plate, Plane glass plate inclined at 45 0,sodium
vapour lamp, travelling microscope, reading lens, black sheet.
PRINCIPLE: This experiment is based on the principle of interference.
NATURE OF INTERFERENCE PATTERN: In this experiment all the fringes are circular in shape, with
central dark fringe( in reflected system only). The fringes are circular due to locus all the points which
are having, constant air film thickness is lie along the circumference of a circle.
FORMULA: The expression for radius of curvature of a given plano-convex lens, in Newton rings
is given by
,B
ge
fP
hy
sic
s,
B
ap
at
la
En
gi
n
ee
rin
g
Co
lle
Here Dm & Dn are the diameters of mth & nth ring respectively.(in c.m)
= Wa ele gth of light sou e used. ( =5893x10-8 c.m)
ap
at
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−
−
=
D
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tm
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to
THEORY :
When light from sodium vapour lamp is allowed to fall directly on to a ordinary plane glass plate
inclined at 450 , it is reflected at 450 ( according to laws reflection and refraction ) and fall normally
(i.e angle of i ide e i = 0 ) onto the system of plane glass plate and plano-convex lens . When
convex surface of plano- convex lens is placed on plane glass plate, it rest at one point, as shown in
fig. The air film thickness between convex surface and plane glass plate is gradually increasing from
the point of contact (where thickness of the film is zero), called wedge shaped film. The light rays
which fall normally onto the system under go first reflection at plano - convex lens surface, and
second reflection from plane glass plate. Since both these light rays are derived from same source,
they possess same wavelength and has a constant phase difference equal to thickness of the air film
at that place. These light rays interfere in the field of view of travelling microscope, producing
interference fringes as concentric circles of alternate bright and dark. This is because, locus of all the
points, which are reflecting at same air film thickness is lie along the circumference of a circle.
PROCEDURE:1) Glass plate and lenses are thoroughly cleaned.
2) First one has to detect the plane glass plate and plano-convex lens. This can be done by shaking the lens
while viewing any object through it.
(i) If the object is seen through the lens is shaking, when the lens is shaking, then that lens is a plano convex
lens.
(ii) If the object seen through the lens is not shaking, when the lens is shaking, then that one is a plane glass
plate.
Now keep the plano-convex lens on plane glass plate and gently rotate. If it stops rotating immediately, then
it means that the plane side of plano-convex lens is rest on the plane glass plate. If it rotates for some time,
then it means the convex side of plano-convex lens is rest on plane glass plate.
3) The glass plate i the Ne to s i gs appa atus is set su h that it akes a a gle of 0 with the direction
of incident light coming from the source. It is the necessary condition for the well illumination of
combination and to allow light rays to fall normally on to that system.
4) The microscope is moved in the vertical direction till the rings are seen distinctly.
5) The center of the fringes is brought symmetrically below the cross wires by adjusting the position of the
lens and the microscope.
6) The microscope is moved in horizontal direction to one side of the fringes such that one of the cross wires
becomes tangential to the 18th ring. Note down the main and vernier scale readings.
at
la
7) Move the microscope and make the cross wire tangential to the 16th, 14th up to 8th ring and on the other
side up to 18th ring. Note down the readings.
Co
lle
ge
,B
ap
8) The radius of curvature of the curved surface of the plano-convex lens is determined using spherometer.
Place the lens with its curved surface upwards on the glass plate. Take the spherometer reading when it just
touches the surface. Remove the lens. Take the reading on the plane surface.
ee
+
gi
n
R=
rin
g
9) Place the spherometer on the note book and gently press to obtain the impression of the three legs of the
spherometer. Join the three points and determine the mean distance between the legs.
‘adius of ur ature ‘ of pla o-convex surface is given by
ap
at
la
En
where = distance between two legs of the spherometer, h = thickness of the lens at the centre
TABLULAR FORM FOR THE DETERMINATION OF DIAMETER OF A RING
S.No
Left
Ring
number
VC x LC
Total
reading
RL= a+b
M.S.R
a
Right
VC x LC
Total
reading
RR= a+b
Diameter of
the ring
D = RL~ RR
cm
D2
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to
fP
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sic
M.S.R
a
s,
B
Readings of travelling microscope
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ep
ar
GRAPH:
Plot a graph by taking ring number on X- axis and corresponding square of the diameter of the ring on Y- axis,
we get a graph as a straight line passing through origin as shown in Fig. below.
‘ alue a also e fou d f o the g aph, taki g the
slope of the straight line
D2
n
PRECAUTIONS:1) Glass plates and lens should be cleaned thoroughly.
2) In order to avoid any error due to back-lash of the screw in the travelling microscope, the micrometer
screw should be moved only in one direction for the measurement of diameter of rings
3) Crosswire should be focused on a bright ring tangentially.
4) Do the calculation in cgs units only.
RESULT: The radius of curvature of given plano - convex lens was found to be _______ cm
DIFFRACTION GRATING
AIM: -To determine the wavelength of spectral lines of mercury spectrum using diffraction grating by
normal incidence method.
APPARATUS:-Plane transmission grating, mercury vapor lamp, spectrometer, grating stand, spirit
level, table lamp and magnifying lens.
PRINCIPLE:- Diffraction phenomenon is the principle of this experiment.
FORMULA:- The wavelength of spectral line is given by
=
gi
n
ee
rin
g
Co
lle
ge
,B
ap
at
la
He e θ is the a gle of diff a tio ( in degrees)
N is u e of uled li es pe e ti ete o g ati g su fa e.
is o de of diff a tio spe t u .
DIAGRAM:
En
WORKING:-
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to
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s,
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ap
at
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Grating refers to an arrangement of set of parallel lines with equal spacing. The optical plane
Diffraction grating that we are using consists of a set of parallel lines (15000 lines per inch) drawn on
an optical surface. These ruled lines are opaque to light or acts as obstacle to light propagation, while
the spaces between them are transparent. When a monochromatic light of a ele gth is i ide t
normally, the diffracted beams at each ruled line interfere with one another producing diffraction
pattern in the field of view of telescope. Since we are using mercury vapor lamp (polychromatic) in
this experiment, the diffraction consists of beautiful VIBGYOR on their either sides of the central
maxima. By measuring angle of diffraction, the wavelength of each color can be determined using the
above expression.
D
NORMAL INCIDENCE PROCEDURE:Normal incidence means the angle of incidence is zero degrees i.e. we have to set both the light ray
and normal to the surface are parallel to each other, and this can be done as follows by using
spectrometer.
1. Release the locks provided at vernier table and telescope
2. Focus the telescope to a distant object and rotate the Rack& Pinion screw till the image
of the distinct object appears clearly.(NOTE: DO NOT CHANGE THE POSITION OF THE SCREW,TILL THE
EXPERIMENT IS OVER.)
3.Bring the telescope in line with collimator and observe the slit through telescope .If the image of
the slit is blurred, then rotate Rack & Pinion of the collimator till slit appears very clear.(NOTE:
DO NOT CHANGE THE POSITION OF THE SCREW,TILL THE EXPERIMENT ISOVER.)
4. Coincide the cross wire with slit image and lock the telescope.
5. Set the position of the vernier table at 0° -0° or 0°-180° and lock the vernier table.
6. Release the telescope and rotate it (either left side or right side) through 90° and lock the telescope.
7. Place the diffraction grating into grating stand and rotate the grating table towards telescope till the
reflected image coincides with the vertical cross-wire. (i.e., angle of incidence is 45°. )
8. Release the vernier table and rotate it through 45° towards collimator and lock it.
9. Release the telescope and observe the diffraction pattern on either side of the central maxima.
MEASUREMENT OF WAVELENGTH:
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,B
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After adjusting for normal incidence the telescope is then rotated towards either left or right side of the
central maxima so as to catch first order spectrum. Let us first move the telescope towards left side of the
central maxima. Now set the position of the telescope such that the intersection of cross wires coincides
with red spectral line and note down the reading in any one of the vernier. (It should be noted that all the
readings should be noted from only one vernier i.e., either from vernier-1 or vernier-2. After noting down
the reading, the telescope is move towards next spectral line, and note down the reading of that spectral
line. Repeat the same process for each spectral line on left side of the central maxima. Now the telescope is
moved in the same direction i.e., towards right side of the central maxima such that the cross-wires coincide
with violet to red spectral line. (If you begin your experiment by moving telescope to the right side first, then
the procedure is repeated by noting the spectral line position from right to left side). The difference between
the eadi gs of spe t al li e o left a d ight is e ual to t i e the a gle of diff a tio
θ a d a ele gth of
spe t al li e is dete i ed afte su stituti g θ i the a o e e tio ed fo ula.
� ~� �
�=
(Degree)
VCXLC
V.C
(Degree)
ap
at
M.“.‘ a la
s,
B
sic
V.C
=
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Red
Orange
Yellow
Green
Blue
Violet
VCXLC
En
Readings of the telescope
Left (Degree)
Right (Degree)
Total
Total
reading
reading
RL=a+b
RR=a+b
(Degree)
M.“.‘ a
(Degree)
Colour of the
spectral line
S.No
gi
n
TABLULAR FORM FOR DETERMINATION OF ANGLE OF DIFFRACTION AND WAVELENGTH:
PRECAUTIONS:
1. Always the grating should be held by the edges. The ruled surface should not be touched.
2. Light from the collimator should be uniformly incident on entire surface of the grating.
RESULT:
The wavelength of all spectral lines of mercury spectrum are calculated and compared with standard
wavelength and found that they are nearly equal.
DETERMINATION OF LASER WAVELENGTH BY DIFFRACTION GRATING
AIM: To determine wavelength of LASER source by using plane transmission grating.
APPARATUS: Diode LASER, power supply,, plane transmission diffraction grating, scale, screen, graph
paper.
FORMULA: The condition for nth order diffraction principle maxima is given by
+
=
−−−−−
���� �+� �� ����� �� ���� ���� �� �����n� �����n�, n �� ����� �� ����������n.
=
From Fig 1
√
+
−−−
,
�ℎ
where � � ℎ �
ℎ
(in c.m)
The expression for wavelength of LASER source from the above expression is given by
+
]Å
la
D �� �����n�� ������n �����n� �n� �����n. (in c.m)
√
at
)[
ap
+
,B
= (
D
FIGURE 1
TABLE FORM
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s,
B
ap
at
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En
gi
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ee
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Co
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THEORY:
We know that grating refers to a set of parallel lines with equal spacing. When such arrangement was
made on a plane glass plate, then it is called optical grating. Each line on the slit is acting as an obstacle
to the light propagation and light undergoes diffraction. The plane transmission diffraction grating used
�n ��� ���������� �� ��n����� �� 5,
��n�� ��� �n��. W���� �� ���� ������ ���� �� � �n� ����� �� ����
���n�����n� ���� �� � . �+� �� ������ �����n� �����n� �� ����� �� ���� ����. W��n LA�E� �ight falls on
grating surface it is diffracted and diffraction spots were observed on either side of central maxima as
shown in Fig. The distance of each order spot from central bright spot must be equal. At one particular
distance between grating and scre�n �����n�� �� ���� D , n��� ���n ��� �����n�� �� ���� ����, �n ����
sides of central maxima. Repeat the same for other distances also.
S.No
Distance between
screen & grating (D)
Distance of nth order from
central maxima
Left
Right
Mean(Xn)
= (
+
)[
√
+
]Å
PRECAUTIONS
1. Clean the grating surface with soft cloth and do not touch the surface with fingers till the experiment
is over.
2. Mark spots of various orders on graph paper with pencil at the center of that spot.
3. Do not see the LASER light with naked eye, because it cause loss of sensation of vision
RESULT: The wavelength of laser light using plane diffraction grating was found to be_____
CHARACTERISTIC CURVES OF A PHOTO CELL
AIM : To draw the characteristic curves of photo voltaic cell
APPARATUS : photo emissive cell mounted inside a blackened wooden box with a wide slit , Ammeter ,
Lamp and Scale arrangement Power supply for D.C, Anode potential Dry Battery 0-45V, a Rheostat a
plug key, a resistance Box and connecting wires.
PRINCIPLE: This experiment is based on principle of photo electric effect
PHOTO ELECTRIC EFFECT: When a light of suitable frequency falls on some metal surface, electrons are
ejected from that surface, without any delay. This effect is called photoelectric effect and the liberated
electrons are called photo electrons.
FORMULA: The maximum velocity of liberated electrons is given by
=√
���� � =C����� �� �n �������n ,
CIRCUIT DIAGRAM:
/
ap
at
la
En
gi
n
ee
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g
Co
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ge
,B
ap
at
la
=Stopping potential, m= Mass of electron
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sic
s,
B
THEORY:
We know that according to photoelectric effect, when a light of suitable frequency falls on some
materials called photo sensitive materials like alkali materials, electrons are ejected from that material,
without any time delay. This effect is called photo electric effect and the liberated electrons are called
����� �������n�. T��� ��n �� ������n�� �n ��� ����� �� E�n����n � ������ �� �������. A������n� �� M��
P��n� � ���n��� ������, ����� �n���� ���� ����� ������ �� ������� �n ����� �� �������� ������� �� energy,
having the value integral multiples of h�(Here �is frequency of light). This packet of energy can also
treat as a particle, called PHOTON. Hence showering of light rays onto a material can be treated as
showering of particles or photons coming from light source. These incident photons transfer their
energy, to the outer most electrons of, atoms of photo sensitive material. Some part of energy of photons
is used to liberate the electrons from that metal atom(called work function of that metal), and
remaining energy is given to the same electron in the form of kinetic energy. This can be expressed
mathematically as
=
+
T�� ����� ���������n �� ���� ������ E�n����n � ����� �������� �������n.
is called work function of that
metal. By virtue of their kinetic energy possessed, the liberated photo electrons in photo cell are able to
reach anode and produce some photo current in the circuit, even in the absence of potential difference
applied(i.e at v=0). With the increase of positive potential given to anode, more and more number of
electrons is collected by anode, and there by photo current increases linearly up to some positive
potential and becomes constant at high value of potentials. This is because, at high value of potentials,
all the produced photo electrons at one particular intensity of light, are collected by anode. When
intensity of light source is increased, more photo current is produced in the circuit. When –ve potential
is to anode, because of repulsion, number of photo electrons reaching towards anode decreases and
leads to decrease in photo current with increase of –ve potential, as shown in Fig2. At a particular –ve
potential, photo current in the circuit becomes zero, called STOPPING POTENTIAL. At stopping potential,
the photo electron having maximum kinetic energy is experiencing maximum repulsion from –ve
potential, and hence unable to reach the anode. Due to this photo current is zero in the circuit. Stopping
potential depends up on kinetic energy of photo electron, which intern depends up on photon energy or
frequency of radiation. Hence stopping potential increases with increase of frequency of radiation, and
independent of intensity of radiation.
.
=
=
=√
/
LAWS OF PHOTO ELECTRIC EMISSION
1. There is no time lag between arrival of photon and emission of electron
2. Photo current increases with increase of intensity of radiation and independent of frequency of
radiation
3. Stopping potential increases with increase of frequency of radiation, independent of intensity of
radiation.
PROCEDURE:
Co
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ge
,B
ap
at
la
Make the connections as shown in the circuit. Keep the light source at a particular distance say 10 cm
from photo cell. Switch on light source and make the light to incident on photo cell. Note down the
photo current when anode potential is zero. Increase the anode potential in steps of 50 mv and note
down the corresponding photo current, until the current reaches to saturation. Now reverse the
potential applied to photo cell. (i.e anode is now at –ve potential & cathode is at +ve potential). Now
increase the reverse voltage potential in steps of 50 mv till the photo current reaches to zero. Note
down the stopping potential at this intensity. Repeat the same procedure when light source is kept at
20cm away from photo cell.
TABLE FORM
At light intensity I1
ee
Photo current
S.No
REVERSE
Applied potential
mV
Photo current
ap
at
la
En
gi
n
S.No
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g
FORWARD
Applied potential
mV
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s,
B
GRAPHS:
Plot the anode potential values on X-axis and anode current valves on Y-axis. We obtain the curves as
shown in the figure. These are known as characteristic curves of a photo voltaic cell.
RESULT: The maximum velocity of photo electron is_______________
SOLAR CELL
AIM: To study the characteristics of a photo voltaic cell ( Solar cell ) and to find Fill factor.
APPARATUS: Solar cell, d.c milli volt meter, d.c micro ammeter, variable resistance box, 100W Lamp,
connecting wires.
PRINCIPLE: This experiment is based on the principle of photo voltaic effect. i.e. When light energy falls on
to a open circuited P-N junction, electron- hole pairs are created, and they were separated by junction
electric field. These separated charges accumulated on P and N regions and leading to create potential
difference across the ends, called Photo – voltaic effect.
FORMULA: Fill factor of a solar cell is given by
=
Fill Factor =
Where Isc = short circuited current ( when resistance in the circuit is zero i.e. R=0 )
Voc = open circuited voltage ( when resistance in the circuit is infinity i.e. ‘= ∞
is actual maximum obtainable power
at
la
= is the ideal power or dummy power output, and
rin
g
Co
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ge
,B
ap
The fill factor is defined as the ratio of the actual maximum obtainable power, to the product of the open
circuit voltage and short circuit current. This is a key parameter in evaluating the performance of solar cells.
Typical commercial solar cells have a fill factor > 0.70. Grade B cells have a fill factor usually between 0.4 to
0.7. The fill factor is, besides efficiency, one of the most significant parameters for the energy yield of a
photovoltaic Cells with a high fill factor have a low equivalent series resistance and a high equivalent shunt
resistance, so less of the current produced by light is dissipated in internal losses.
sic
s,
B
ap
at
la
En
gi
n
ee
CIRCUIT DIAMGRAM:
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THEORY:A solar cell (also called photovoltaic cell or photoelectric cell) is a solid state electrical device that
converts the energy of light directly into electricity by the photovoltaic effect. Assemblies of solar cells are
used to make solar modules which are used to capture energy from sunlight. When multiple modules are
assembled together, the resulting integrated group of modules all oriented in one plane is referred to in the
solar industry as a solar panel. The electrical energy generated from solar modules, referred to as solar
power, is an example of solar energy. A solar cell is basically a P-N Junction semiconductor diode, usually
made from silicon. The thickness of P- region and N-region are kept very small so that electrons and holes
generated near the surface can diffuse across the junction before recombination takes place. A heavy doping
of p– and n- regions is recommended to obtain a large photo voltage. When light falls on a pn- junction
diode, photons collide with valence electrons,
and impart them sufficient energy enabling them to leave their parent atom. Thus electron-hole pairs are
generated in both the p- and n- sides of the junction. These electrons and holes reach the depletion region
by diffusion and are then separated by the strong barrier field existing there. However, the minority carrier
electrons in the p-side slide down the potential barrier to reach the n-side, and holes in the n-side move to
the p-side. Their flow continues the minority current, which is directly proportional to the illumination, and
also depends on the surface area being exposed to light. The accumulation of electrons and holes on the two
sides of the junction give rise to an open circuited voltage V oc , which is a function of illumination. The open
circuit voltage for a silicon solar cell is typically 0.6 volt and short circuit current is about 40ma/cm2.
EXPERIMENTAL PROCEDURE
1.Keep the solar cell in the sun light for 15 to 20 minutes.
2. Adjust the rheostat position for resistance so that the volt meter reads zero. This is the short circuit
connection. Note down the value of the current as short circuited current, Isc. Disconnect the rheostat from
circuit, then voltmeter shows maximum reading, note down the value of voltage as open circuit voltage ( V oc
)
3. Increase the resistance by varying the rheostat slowly and note down the readings of current and voltage
till a maximum voltage is read. Ensure to take at least 15–20 readings in this region.
4. Repeat the experiment for another intensity of the illumination source.
5. Tabulate all readings in Table 1. Calculate the power using the relation, P = V xI.
6. Plot I vs. V with Isc on the current axis at the zero volt position and Voc on the voltage axis at the zero
current (see Figure 5.)
7. Identify the maximum power point Pm on each plot. Calculate the series resistance of the solar cell using
the formula as follows : RS = [ DV/DI ].
at
la
8. To see the performance of the cell calculate fill factor (FT) of the cell, which can be expressed by the
formula, FF = [ PMax/Isc x Voc ].
Volt meter
Ammeter
V (Volt)
I (ma)
Co
lle
Resistance in
ohms (R)
Power =IxV watt
ee
rin
g
S.No
ge
Reading of volt meter & ammeter
,B
ap
TABLE FORM FOR MEASUREMENT OF POWER
gi
n
GRAPH:
En
Draw a graph by taking current values on X-axis and corresponding voltage values on Y-axis, we get the
sic
s,
B
ap
at
la
following nature, as shown in Fig. Also draw two straight lines at V oc and Isc. The area spanned by Isc x Vocis
the dummy power or ideal power produced from the circuit.
V
I(Current)
Isc
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to
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Voc
D
PRECAUTIONS:
1. Expose the solar cell to sun light for few minutes, for attaining stable values of current and voltage
2. A resistance in the cell circuit should be introduced so that the current does not exceed the safe operating
limit.
RESULT: The characteristic curve for solar cell was drawn and fill factor was found to be______
DETERMINATION OF ENERGY GAP OF A SEMICONDUCTOR
AIM: To determine energy gap of a semiconductor.
APPARATUS: P-N diode, DC regulated power supply, Voltmeter, Milli ammeter, 1 KW resistor, Beaker,
Thermometer, Heater.
PRINCIPLE: Semiconductor energy gap is determined by passing small forward current
through Si, Ge, GaAsAl, GaAsP, SiC junction diodes. The junction voltage variation is studied with
temperature. From temperature versus junction voltage curve, energy gap is determined.
FORMULA: A pn crystal is called junction diode. Diode can be forward or reverse biased using a voltage
source. During forward bias forward current flows through the diode. The forward current is given by
=
− ]
IF is called forward current
IR is called reverse current or reverse saturation current
q is electronic charge e =1.6x10-19 Coulomb
η is alled idealit fa to a ies et ee a d .
k is Boltzman constant = 1.38x10-23J/K
T is temperature in degree Kelvin.
When the diode is reverse biased negligible reverse current flows through the diode. The reverse current is
given by
−
(
⁄
)
rin
g
=
Co
lle
ge
,B
ap
at
la
Where
⁄
[
{
−
ap
at
la
⁄
s,
B
=
En
gi
n
ee
The constant B appearing in equation 2 is a constant connected with the structure or the area of the
depletion region.
Substituting equation 2 in equation 1, we get
⁄
=
{
}{
⁄
⁄
− }
− }
ar
tm
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to
fP
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sic
Taking natural logarithm on both sides, we get the following expression for junction voltage verses
temperature.
=
=
+
−[
]
D
ep
The above Eq represents a straight line, and its slope, Y- intercept are given by
=−
[
]
=
Energy gap EG is determined from Y-intercept at T= 0K i.e
EG = q Yintercept in Joules.
We know that 1eV= 1.6x10-19 Joules. ⇒ J���� =
.6�
−19
∴ EG = q Yintercept {
Circuit diagram
.6�
−19
} eV
⇒ EG = Yintercept in eV (since q =1.6x10-19 Coulomb)
at
la
THEORY:
In an atom electron occupy distinct energy levels. When atoms join to make a solid, the allowed energy
levels are grouped into bands. The bands are separated by regions of energy levels that the electrons are
forbidden to be in. These regions are called forbidden Energy gaps or band gaps. Energy bands and the
forbidden energy gap is illustrated in figure 1. The electrons of the outermost shell of an atom are the
valence electrons. These occupy the valence band. Any electrons in the conduction band are not attached
to any single atom, but are free to move through the material when driven by an external electric field.
D
ep
ar
tm
en
to
fP
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sic
s,
B
ap
at
la
En
gi
n
ee
rin
g
Co
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ge
,B
ap
In a metal such as copper, the valence and conduction bands overlap as illustrated in figure 2a. There is no
forbidden energy gap and electrons in the topmost levels are free to absorb energy and move to higher
energy levels within the conduction band. Thus the electrons are free to move under the influence of an
electric field and conduction is possible. These materials are referred to as conductors. In an insulator such
as silicon dioxide (SiO2), the conduction band is separated from the valence band by a large energy gap of 9.0
eV. All energy levels in the valance band are occupied and all the energy levels in the conduction band are
empty. It would take 9.0 eV to move an electron from the valence band to the conduction band and small
electric fields would not be sufficient to provide the energy, so SiO 2 does not conduct electrons and is called
an insulator. Notice the large energy gap shown in figure 2b. Semiconductors are similar to the insulators
insofar as they do have an energy gap only the energy gap for a semiconductor is much smaller ex. Silicon's
energy gap is 1.1 eV and Germanium's energy gap is 0.7 eV at 300 °K. These are pure intrinsic
semiconductors. Observe the energy gap in figure 2 c.
For finite temperatures, a probability exists that electrons from the top of the valence band in an intrinsic
semiconductor will be thermally excited across the energy gap into the conduction band. The vacant spaces
left by the electrons which have left the valence band are called holes which also contribute to the
conduction because electrons can easily move into the vacancies. If an electric field is applied, the electrons
flow in one direction and the holes move in the opposite direction. The holes act as a positive charge
(deficiency of negative charge) so the direction of current (effective positive charge) is in the same
direction. For pure silicon at 300 °K, the number of electrons residing in the conduction band as a result of
thermal excitement from the valence band is 1.4 x 1010 /cm3.
At absolute zero degree temperature, semiconductors are pure insulators. As the temperature is increased
thermal energy create vibrations in crystal lattice and few electrons, which acquire sufficient vibrational
En
gi
n
ee
rin
g
Co
lle
ge
,B
ap
at
la
energy break their covalent bond, become free, and move to the conduction band. The energy required to
rapture the covalent bond is designated as energy gap EG and termed as energy gap or band gap energy.
Energy less than EG is not acceptable or one cannot have partially ruptured bond, hence this energy is also
called as forbidden gap energy. In silicon crystal, at room temperature (300ºK) about 1019 covalent bonds are
broken per cubic meter out of 1029 atoms. It is only one atom in 1010 exits with broken bond. This is less than
one atom per thousand atoms on each of the three-crystal axis. The electrons that are freed take part in
conduction and the material becomes semiconductor. Such a semiconductor is known as intrinsic
semiconductor. The resistivity of such a semiconductor falls in the range of 0.4 to 2500 ohmmeter. As the
temperature increases above room temperature more and more covalent bonds are broken and conduction
increase rapidly and resistivity fall. Intrinsic semiconductors are useless for electronics applications because
of their low conduction at room temperature. Adding impurity atom from the third or fifth group elements
can increase the conduction. This process of adding impure atom is known as doping and the doped
semiconductor becomes extrinsic semiconductor. Addition of impurity from the fifth group element result in
n-type semiconductor and addition of impurity atom from third group results in p-type semiconductor.
Energy gap is a very important parameter of semiconductor that decides its applicability. Determination of
semiconductor energy gap is an important experiment in physics lab. Pure semiconductors or intrinsic
semiconductors are not available easily for measurements. Extrinsic semiconductors are easily available for
EG measurements.
PROCEDURE:
To determine the energy gap EG a small constant current of the order of 100 –
A is passed through the
diode at various temperatures. The voltages developed at the junction are noted. The junction voltage versus
temperature graph is drawn. From the straight-line graph, Y intercept gives the EG directly in electron volt.
From the slope, constant B is calculated using equation. For small forward current of the order of hundreds
of microampere e slope is unity. Which indicate that the graphs for different diodes are all parallel and the
constant B is independent of diode material, it depends only on the forward current, hence it is connected
with majority carriers.
Temp.of the bath
(Centigrade)
Temp.of the bath (Kelvin)
Junction voltage (mV)
sic
S.No
s,
B
ap
at
la
TABLE FORM FOR THE MEASUREMENT OF JUNCTION VOLTAGE
Constant current passing through the semiconductor/diode is_____________
tm
en
to
fP
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1
2
D
ep
ar
GRAPH:
A graph is drawn between temperature of the bath on X-axis and corresponding junction voltage values on
Y-axis we get a straight line as shown in Fig. below.
RESULT: Energy gap of given semiconductor diode is ____________
HALL EFFECT
Aim: To determine the hall coefficient (KH), mobility of charge carriers (µ) and concentration of charge
carriers(n) in a given material
Apparatus: Hall probe, Hall effect setup for measurement of current and voltage, electro-magnet, constant
dc power supply to electro-magnet and Gauss meter.
Hall Effect: When magnetic field is applied perpendicular to a current carrying conductor, then a voltage is
developed in a direction both perpendicular to charge flow and applied magnetic field direction ; is known as
Hall effect. The developed voltage is known as Hall voltage(vH).
,B
ap
at
la
CIRCUIT DIAGRAM
rin
g
,
ee
&
gi
n
�−
Co
lle
=
Where e is the harge of ele tro ,
=
ge
FORMULA:
=
.
=
−
=
.
−
�
(in Tesla)
fP
(in volts)
hy
=
sic
s,
B
���� =
ap
at
la
En
=
tm
en
to
Mobility of charge carriers (µ)= KH σ (in m2/volt-Sec)
ar
here σ = o du ti it of sa ple = /ρ
D
ep
ρ= resisti it of sa ple, gi e
=
=
= ��� −
=
" "=
=
THEORY:
Let us consider a rectangular plate of a conductor or semiconductor placed with its thickness along zdirection, the length along the x-direction and width along y-direction as shown in the above Figure1. Let a
voltage be applied along x-direction such that it produce a current Ix, given
by =
ℎ
�
� & �
�
.Now let a magnetic field
is
applied along Z-direction. The applied magnetic field deflects the charge carriers towards positive Ydi e tio , a d di e tio of defle tio fo e a e k o
f o Fle i g s left ha d ule. If the gi e sa ple
contain both +ve and –ve charges, then both of them will be deflected towards same side, leading to
creation of potential difference between top and bottom face of the sample(i.e. along Y-direction), called
hall voltage. After creation of potential difference charged particles moving along x- direction do not under
go any deviation from magnetic field, and move in straight path. This is because the deflection force from
magnetic field is balanced by force exerted by Hall electric field (i.e., force of repulsion exerted by already
settled charges on the top surface of the sample).
At equilibrium the above two mentioned forces are equal.
=
=>
=
.
=
(
)
=
(
)
=
The term is is called Hall coefficient denoted by RH. It is numerically equal to the developed Hall electric
field when unit strength current is passing through the sample, in the presence of unit strength of externally
applied magnetic field.
We k o that the elatio et ee E, V a d d is E = V/d
=>
=>
=
=>
=
=
[
[
=
= ]
=
]
ge
�
Co
lle
=> µ =
,B
ap
at
la
From the above expression we can calculate density of charged carriers.
We k o that o du ti it of the sa ple σ = eµ
Where µ is mobility of charged carrier. It is defined as the drift velocity acquired by charged carrier under the
application of unit electric field.
s,
B
ap
at
la
En
gi
n
ee
rin
g
=>µ = �� �
PRACTICAL:
In the experiment Hall probe consists of a semiconductor sample in square shape having four pressure
contacts as shown in fig. The two opposite ends are connected by a same color wire.
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1.For the measurement of resistivity of sample connect one red and one green wire to current terminals,
and other two wires connected to voltage terminals of Hall effect setup. Measure the voltage (Vx) for each
current value and tabulate them.
2.Connect one set of same colour wires to current terminals and other set of colour wires to voltage
terminals of Hall effect setup. Measure the error voltage (i.e., voltage in the absence of magnetic field) at
different values of current passing through the sample. Measure the transverse voltage or Hall voltage in the
presence of magnetic field for the same values of current passing through the sample, for the measurement
of error voltage. The difference in the two voltages is the correct Hall voltage.
Table – I:FOR THE MEASUREMENT OF RESISTIVITY
S.No.
Current
Ix (mA)
Voltage
Vx (mV)
Table – II: FOR THE MEASUREMENT OF HALL VOLTAGE.
Transverse voltage(OR)HALL VOLTAGE
S.No. Current
Ix
Model graph:
With out
magnetic field
a
With
magnetic field
True Transversevoltage
(OR)
True Hall voltage
Vy= b-a
(mv)
(1) Plot the graph between Ix on x-axis, Vx on y-axis, we get a straight line.
(2) Plot the graph between Ix on x-axis, VH on y-axis we get a straight line.
Vx
IxIx
Ix
CALCULATION PART:
(1).Find the slope of straight line in the graph (i.e., IxVsVx) and it is equal to resistance
( R ) of the sample.
(4). Find the slope of
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�
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µ =
gi
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.
(7).
= ]Ω−
graph, put this value in
=
=
[
/
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(5).
−
=
ap
Ω−
=
,B
(3).Conductivity � =
=
ge
(2). We know that Resistivity
−
�
s,
B
Sample dimensions are l = b = 5mm = 5X10-3m, t =0.5mm = 0.5X10-3m
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PRECAUTIONS:
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1 Increase slowly the current through electromagnet from power supply (max up to 2A).
to
2 Before to switch off power supply, reduce current to zero and the switch off.
1.
2.
3.
4.
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RESULT:
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3 Keep the probe in the Gauss meter at the center of pole pieces and rotate at till it shows maximum reading
for the measurement of magnetic field.
=
−−−−−−−Ω−
� =
µ =
/��
−−−−−−Ω−
−
−−−−−−−−
�=−−−−−−
/
−
RESONANCE IN LCR CIRCUIT
AIM: To study resonance effect in series LCR circuit and quality factor.
APPARATUS: A signal generator, inductor, capacitor, ammeter, resistors, AC milli voltmeter.
FORMULA: The expression for resonant frequency of L-C-R circuit is given by
1
Hz
fr 
2 LC
���� L �� �n�����n�� �� �n������ �n ��n���
C �� ��������n�� �� ��������� �n F�����
� �� �������n�� �� ��� �������� �n O���
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BASIC METHODOLOGY:
In the series LCR circuit, an inductor (L), capacitor (C) and resistance(R) are connected in series with a
variable frequency sinusoidal emf source and the voltage across the resistance is measured. As the
frequency is varied, the current in the circuit (and hence the voltage across R) becomes maximum at the
1
at a particular frequency called resonance frequency f r 
. In the parallel LCR circuit there is a
2 LC
minimum of the current at the resonance frequency.
THEORY:Circuits containing an inductor L, a capacitor C, and a resistor R, have special characteristics useful in
many applications. Their frequency characteristics (impedance, voltage, or current vs. frequency) have
a sharp maximum or minimum at certain frequencies. These circuits can hence be used for selecting or
rejecting specific frequencies and are also called tuning circuits. These circuits are therefore very
important in the operation of television receivers, radio receivers, and transmitters. In this section, we
will present two types of LCR circuits, viz., series and parallel, and also discuss the formulae applicable
for typical resonant circuits. A series LCR circuit includes a series combination of an inductor, resistor
and capacitor whereas; a parallel LCR circuit contains a parallel combination of inductor and capacitor
with the resistance placed in series with the inductor. Both series and parallel resonant circuits may be
found in radio receivers and transmitters.
SERIES RESONANCE CIRCUIT:-
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When an alternating e.m.f � = � � � 0 was applied to circuit having an inductance L, capacitance C
and resistance R in series as shown in fig. The current in the circuit at any instant of time t is given by
the following equation
� =� � � −�
Where it can also be proved that the maximum current � is
=
√� + � −
�
−−−−−
From the above expression(1)the impedance of circuit is given by is
= √� + (� −
�
)
The L - C - R series circuit has a very large capacitive reactance (� ) at low frequencies and a very large
inductance reactance (� ) at high frequencies. So at a particular frequency, the total reactance in the
circuit is zero (� = � . Under this situation, the resultant impedance of the circuit is minimum. The
particular frequency of A.C at which impedance of a series L - C - R circuit becomes minimum is called
the resonant frequency and the circuit is called as series resonant circuit.
At resonance frequency
� =
�
=> � =
√
=>
=
�=
√
The above equation shows that the resonant frequency depends on the product of L and C and does not
depend on R. The variation of the peak value of current with the frequency of the applied e.m.f is shown in
Fig.
Let f1 and f2 be these limiting values of frequency. Then the width of the band is
� = −
The quality factor is defined as
=
=
−
ap
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Q-factor is also defined in terms of reactance and resistance of the circuit at resonance,
�
=
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,B
PROCEDURE:
1. The series and parallel LCR circuits are to be connected as shown in fig 1 & fig 2.
2. Set the inductance of the variable inductance value and the capacitances the variable capacitor to low
1
values ( L ~ 0.01H , C ~ 0.1 µ F ) so that the resonant frequency f r 
is of order of a few kHz .
2 LC
3. Choose the scale of the AC milli voltmeter so that the expected resonance occurs at approximately the
middle of the scale.
4. Vary the frequency of the oscillator and record the voltage across the resistor.
5. Repeat (for both series and parallel LCR circuits) fir three values of the resistor (say R = 100, 200
&300 ).
TABLE FORM
L = _______________________ mH C = _______________________ µF.
Voltage across resistor (R)
Applied frequency
S.No
f Hz
R=
R=
R=
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RESULT :
Estimated value of Q for series resonance from graph :
Resonance frequency for series LCR circuit =________________Hz
FIELD ALONG THE AXIS OF A CUURRENT CARRYING CIRCULAR COIL
AIM : To determine the magnetic field along the axis of a current circular coil, using Stewart-Gees apparatus.
APPARATUS: Stewart-Gees apparatus, D.C. Power supply, magnetometer, commutator,
rheostat, ammeter.
Working formula: The magnitude of the field B along with the axis of a coil is given by
=
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+
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s,
B
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,B
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Where n = number of turns in the coil.
a = radius of the coil (in c.m)
i = current in ampere flowing in the coil (in Amperes)
x = distance of the point from the centre of the coil. (in c.m)
-7
µ0 = permeability of free space (µ0 =
N-m2 /Ampere2)
In this experiment, the coil is oriented such that, the plane of the coil is along the magnetic meridian. This
can achieved by arranging the plane of the coil parallel to magnetic needle in the magnetometer. When
there was no current through the coil, needle in the magnetometer is rest along geographic north and south
direction (neglecting a gle of de li atio , due ea th s ag eti field. Whe u e t is passi g th ough the
circular coil, magnetic field is produced along the axis of coil i.e along geographic east and west directions.
Now the needle in the magnetometer is under the influence of t o ag eti fields, o e is ea th s ag eti
field acting along north to south & the other is magnetic field produced along east-west direction due to
current carrying coil.) acting perpendicular to one another. Due to the influence of above said two fields,
needle in the magnetometer is deflected to an angle � ith espe t to ea th s ag eti field as sho i Fig
shown below. According to tangent law, magnetic field along the axis of circular coil is given by � =
��
�.Usually�� horizontal co po e t of ea th s ag eti field he egle ti g a gle of de li atio .
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CIRCUIT DIAGRAM
DESCRIPTION:
The apparatus consists of a circular coil mounted perpendicular to the base as shown in fig. A sliding
compass box is mounted on aluminum rails graded with a scale on the rails, so that the compass is always
slides on the axis of the coil, and distance from the center of the coil can be measured.
PROCEDURE: 1. Place the magnetometer compass box on the sliding bench so that its magnetic needle is at the centre of
the coil. By rotating the whole apparatus in the horizontal plane, set the coil in the magnetic meridian
roughly. In this case the coil, needle and its image all lie in the same vertical plane. Rotate the compass box
till the pointer ends read 0 – 0 on the circular scale.
2. To set the coil exactly in the magnetic meridian set up the electrical connections as shown in Fig. Send the
current in one direction with the help of commutator and note down the deflection of the needle. Now
reverse the direction of the current and again note down the deflection. If the deflections are equal then the
coil is in magnetic meridian. Otherwise turn the apparatus a little, adjust pointer ends to read 0 – 0 till these
deflections become equal.
3. Using rheostat (Rh) adjust the current such that the deflection is between 50 0 – 600 degrees is produced
in the compass needle placed at the centre of the coil. Read both the ends of the pointer. Reverse the
direction of the current and again read both the ends of the mean deflection at x =0.
4. Now shift the compass needle through 5 cm each time along the axis of the coil and for each position note
down the mean deflection. Continue the process till the compass box reaches the end of the bench.
5. Repeat the measurements exactly in the same manner on the other side of the coil.
6* Keep it mind that same current should flow at all observations. If there is any variation in current due to
fluctuation, adjust the rheostat position to get that same value of current.
TABLE FO‘M FO‘ THE DETE‘MINATION OF B VALUE“.
Tesla
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+
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=
θ8
(
H
θ5 θ6 θ7
ap
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θ4
E
θ3
Reverse
8
θ1 θ2
Direct
5
Reverse
W
Direct
West side of the coil
(degrees)
gi
n
θ e=A erage of θ to θ
er
in of θ to θ ) (deg)
θ= A erage
g
Co
lTale θ
ge
B = B Ta θ, Tesla
Ba
pa
tla
East side of the coil
(degrees)
θE=A erage of θ1 to θ4
S.No
Distance of each point from
e ter of the ir ular oil
Deflections in magnetometer
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s,
B
GRAPH: Plot g aph taki g
alo g X-a is, a d ta θ along Y- axis, and then we get a bell shaped graph as
shown in Fig. below. The nature of the graph is symmetrical about Y- axis.
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PRECAUTIONS: -
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1) The coil should be carefully adjusted in the magnetic meridian.
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2) All the magnetic materials and current carrying conductors
should be at a considerable distance from the apparatus.
3) The current passed in the coil should be of such a value as to
produce a deflection of nearly 50o -60o
WE““T
EA“T
5) Parallax should be removed while reading the position of the pointer. Both ends of the pointer should be
read.
6) The curve should be drawn smooth.
7) The pointer ends should be at zero each time before sending the current through the coil. If they are not
at zero, the top of the glass cover should be gently tapped to bring them to zero.
RESULT:
It was observed that magnetic field along the axis of a circular was found to be decreasing with increase of
distance from center of circular coil. Also the value of magnetic field from above two formula was found be
nearly equal.