Download Current Electricity

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Current
Electricity
CURRENT ELECTRICITY
Current Electricity
All metals contain free electrons, which can move through the metal under the action of
electric force. The electric current in a conductor is the movement of the free electrons
from one point to another. If two conductors are charged to different potentials and are
connected by a conducting wire, neutralization of charge takes place through the wire
from the conductor at the higher potential to the conductor at lower potential. This flow
of charge in a definite direction constitutes electric current.
Current strength in a conductor is defined as the rate of flow of charge across any cross
-section of the conductor.
If a charge cq' flows across a conductor in a time *t* seconds, the current I is given by,
u.
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Electric current is a scalar quantity eventhough it 2 has magnitude and direction. ->
Unit
In S.I. ampere (A) or coulomb second ''(Cs'1) C.GS. statampere.
1 ampere =
1 coulomb
1 second
Currentthrough aconductoris said'to beone ampere, if one coulomb ofchargeflows at
any cross-section of the conductor in one second
Conventionally the direction of current flow is taken to be the direction of flow of
positive charge. The electron flow is opposite to the conventional current.
CURRENT DENSITY (j )
Current density at a point in a conductor is defined as the amount of current flowing
through unit area of the conductor around that point; provided the area is held normal to
the current direction.
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Current density is a vector quantity.
The direction of current density is same as the
direction of current.
Drift Velocity (vd)
The velocity with which the free electrons get drifted towards the positive terminal, under
the action of the applied electric field is called the drift velocity of the free electrons. The
drift velocity is very small and ranging from I0-4to lO"5 ms-1.
0
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Drift Velocity and Current Density
E—>
Consider a conductor of length V and area of cross section A. Let 'n' be the number of
free electrons per unit volume. When an electric field is applied, the electrons are drifted
from left to right with
a velocity vrf.
Total volume of the container=A x / Total number of electrons contained = nA/ Total
charge enclosed, q = neA/
Electric current, I = ~ = neAj I = neAv.
a
Current density, j = —
A
Drift Velocity and Relaxation Time
When an electric field E is applied across the conductor, a force is setup. Let m be the
mass of the electron,
Force exerted on each electron, F = - eE (Coulomb force is opposite to electric field)
Acceleration of the free electron,
-eE m
m
=F
(1)
But acceleration lasts for a very short time and is lost in the next collision with the
positive ion. If T represents the average time between successive collision, the additional
velocity (drift velocity) acquired by the electron,
0 + ax T
(2)
-eE
m
ie., v
(di
MOBILITY
Mobility is defined as the ratio of magnitude
of drift velocity to electric field strength
Cu rrent Electricity
Ohm's Law If A- !,/= 1 then P=R
George Simon Ohm in 1826 proposed a most Q
of a con-
Hence the resistivity of the material
fundamental law of electricity known as Ohm's law. UJ ductor is defined as the
resistance of the conductor Ohm's law states that the current (I) flowing * of unit length
and unit area of cross section.
through a conductor is directly proportional to «l Unit
the p.d. (V) across the ends of the conductor, pro- S* ,
(^ \
onm m
•j j I • i
j-,r .L
j , i*
(& rn) vided physical conditions of the
conductor such
^
'
as temperature, mechanical strain etc are kept Ul Conductivity (CT)
constant. Q Conductivity of a material is defined as the
ie la V OR
Va 1
"1 reciprocal of the resistivity.
V'
1 -=R
*=—
I'
P
a constant known as resistance of the conductor.
Unit: - ohnr1 m'1 or siemen m~'.
Resistance (R) It is a constant for the material.
Resistance of a conductor is defined as the jj Conductance (G)
ratio of the potential difference (V) applied to &
Conductance of a conductor is
defined as the the current (I) flowing through the conductor.
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reciprocal of its
resistance.
mi
v£
1R=-
£
G=-
1R
Unit jjjj Unit : mho or siemen or ohm"1.
i. SI -ohm (fi) 0
It varies from conductor to conductor.
ii. C.G.S. -> stat ohm or e. s. u of resistance "* DIFFERENCE BETWEEN ohm
metre AND
Jvolt OHMHMETER
1 ampere ohm metre is the S.I. unit of resistivity of a material.
The resistance of the conductor is said to be Ohm-meter is an instrument used to measure
resistance.
one ohm, if one ampere of current flows through perive Qhm's Law
it, when a p.d. of one volt is applied across the ( RELATION ^^5^ RESlglANcEAND
C0
g influence of electric field E, each free The resistance of a conductor depends upon
the -J electron in a conductor experiences a Coulomb force
following factors S eE in a direction opposite to the field. Hence acceli. It is d.rectly proportional to the length of the eration of each electron fa
conductor
; ffi
Roc/ ........ (1) O
a
= Z^I = fX ——— (1)
ii. His inversely proportional to the area of cross m
section of the conductor — V
} [Since E- —— ]
"T """" ^ where mis the mass of an electron, '/'the length
...-,..
,
....
, . of the conductor and V the p.d. across the conducm. The temperature of the conductor. .„ . ,
,
.
. r ,
, .. , .
! T ls
relaxatlon tlme then drlft velocit of
iv. The nature of the material of the conductor f f
^
'
*
From(l)&(2)
' *»«'««>»»
/ v _.
*
v.-.^ ——— (2)
(2) Rocl
nAe2VT R = P! — j where the constant of propor- *
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Current
"
nAev
d
I~
~
^
tionality p is called electrical resistivity or specific H ( nAe2 T\r resistance of the
conductor.
O
i.e., I - I m^ J
(3) Its value
depends upon the nature of the material ^ of the conductor and its temperature.
2
By Ohm's Law, I a
Current
Comparing equatior 1 V V nr I ne
v or
*
Ml
n
f\
QK
VV
Ul
is (3) and (4) we get,
JJj 2Ar
*
R
ml
ti»
w
ml
*
ie
R
I.e.,
Ix -
f
^
n
V
2 *
^'
Z
ne AT
Hence resistance R
"*
cci ———(a)
T
RA
m
also from equation 5, ne2T
P°
—I
Q
c-
CM
W
— ....... (b)
n*
G
S™
T
U.
ml
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Electricity
If R, and Rj are the resistance of a given conductoratt,0Candt20C,
a=
R,t2-R2t,
For metals* a * is positive,
For insulators and semiconductors' a.' is negative.
For alloys such as manganin, constantan etc.,, a (is very small and hence these alloys are used
for making standard resistance coils.
B
rti uuiiMaiii icmueiaiuit
-> .
~ ^uiisiaiii
ne tA
called the resistance of the conductor. (a) & (b) shows that an increase of temperature
increases the number of collision, resulting in
the decrease of col lision time (T) . Hence resistance (resistivity) increases with temp.
Temperature Dependence of Resistance The resistance of a metallic conductor is given by
ml
9
POSITIVEZERO
> e.g. Metals (Al, Cu, Fe etc) Resistance of the metal increases with temperature
c———'
NEGATIVE-*1
e.g. Alloy (manganin, constantan, nichrome etc) Resistance of alloys do not vary appreciably with
temperature
;.jz. Semiconductor
Rne
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An increase of temperature increases the number collision resulting in the decrease of
relaxation
time (t). Hence the resistance increases.
The resistance R of a conductor at t°C is given by the relation
R = R0 (l+ctt+p.t2)
where R0 is the resistance at 0°C, Ot and p are constants of the material of the conductor. For
small ranges of temperature p is very very small.
/.R = R0(l+at)
_R-RQ flC R t * caH®d temperature coefficient Ijj
MM
of resistance. £
The temperature coefficient of resistance of the material of a conductor is defined as the
in- JJj crease in resistance per unit degree rise of temp 0 to its resistance at 0°C. ^ Unit.
Per degree celsius (°C~') or K"1
{carbon, silicon, Ge. selenium etc)
Resistance of semiconductor decreases with temperature
TEMPERATURE COEFFICIENT OF RESISTIVITY.
The temperature dependence of resistivity of a metal is given by the relation .
Where p - p 0 are the resistivity at T and To respectively and a r is called temp coefficient
of resistivity.
a=
TJ 'Po(dT) Thus coefficient of resistivity is defined as the fracQ ill
tional change in resistivity (~~) per unit change in
r °
temperature (dT)
For insulators and semiconductors, resistivity increases exponentially with decreasing
temperature and given as,
E - Forbidden energy gap ,k - Boltzmann constant
s
T - Absolute temperature
Current Conductors. Insulators and Semiconductors
Substances having free electrons, allow the electric current to pass through them. Such
substances are called conductors. Metals, are good conductors of electricity.
Eg: silver is the best), gold, copper, aluminium etc.
Substances in which there are no free electrons, do not allow the electric current to pass
through them. Such substances are called insulators. Non-metals, paper, wood etc., are some
insulators.
semiconductors behave like insulators at very low temperature and behave like conductors at
higher temperature. In semiconductors, current is due to the flow of free electrons and holes.
Ohmic and Non - Ohmic Conductors
Ohmic conductors are those conductors which obey Ohm's law. For such conductors the
graph between p.d. and current is a straight line.
e.g. silver, copper, aluminium etc.
Those which do not obey Ohm's law are called non - Ohmic conductors. For such conductors,
the graph between p.d. and current is not a straight line.
e.g. Semiconductor, electrolyte.
Electricity
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4.2 K-> TEMPERATURE
Reverse
Forward characteristics
V
The figure represents the V-I characteristics of a semiconductor diode (non-Ohmic
substance)
The relation between V and I is not linear. The relation between V and I depends on the sign
qfV.
The relation between V and I is not unique, i.e., I may have more than one value for a given
value of V.
Superconductivity
Certain substances lose their electrical re-sistivity at low temperature. These substances are
called superconductors.
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When the temperature of a metallic conductor is decreased, the resistivity at first decreases
regularly. At a particular temperature called the critical temperature or super conducting
point, resistance suddenly falls to zero. This phenomenon is called superconductivity. This
phenomenon was first observed by Kamerlingh Onnes.
e.g. Mercury at critical temperature 4.2K, lead at 7.25 K, Niobium at 9.22 K become
superconductors. Note
Since the resistance of a superconducting material is zero, current once established in
a superconducting ring will continue itself almost indefinitely. But if the temperature
is increased slightly above the superconducting point, the current drops to zero.
Application
i. Used for making very strong electromagnets
ii. Used to produce very high speed computers.
iii. Used for the transmission of electric power. Thermistors
A thermistor is a heat sensitive device whose
resistivity changes very rapidly with change
in temperature.
A thermistor differs from an ordinry resistance
in the following ways
i. The resistance of a thermistor changes very rapidly with change of temperature, ii. The
temperature coefficient of a thermistor is
very high, iii. The temperature coefficient of a thermistor can
be both positive and negative. The thermistor
having negative temperature coefficient find a
variety of application in practice. Uses i. Thermistors are used for voltage
stabilisation,
temperature control and remote sensing, ii.
Thermistors are used to detect temperature
change and to measure very low temperature
(-10K)
Current
COLOUR CODE OF RESISTORS.
Resistance of various values are used in electrical and electronic circuits. Colour code is used to
determine the value of the resistance and percentage reliability (% oftelerence).
There are three coloured bands on each resistance to indicates its value. The first two bands from
one end indicate their corresponding digits while colour of the third band gives the power often
with which the value has to be multiplied to get the resistance value in ohm.
Combination of Resistances
i.
Resistors in series
R
A number 6f resistors are said to be in series, if they are connected end to end as
shown in the figure. The current will be same in all the resistors. But the p.d. across
each will be different.
Let the three resistors are connected in series (as shown in the fig) between the points A and
B. Let V be the p.d. between A and B. The current through the resistors is the same.
p.d. across Rp V, = IR, .......... (1)
p.d. across R^, V2 = IR^ .......... (2)
p.d. across R.J, V3 = IB^ .......... (3)
Total p,d. across A and B is, v = V . + V + V (4\
12
3 ********* V/
If R is the equivalent resistance of R,, R,, then
V - IR .......... (5)
and
IR = IR
+ IR2 + IR,,
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Electricity then 1 Resistors in Parallel
a)
*••*
5
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COLOUR
VALUE
DECIMAL
MULTIPLIER
Black
0
10°
Brown
1
10'
Red
2
102
Orange
3
HP
0
UI
Yellow
4
104
K
Green
5
10s
mm
Blue
6
106
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Violet
1
107
S
Grey
8
10"
White
9
109
Silver
io-2
TOLERENC
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MM
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10%
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Gold
10-'
No colour
5%
20%
A number of resistors are said to be in parallel if they are connected across same point as
shown in H fig. The p.d. across all resistors will be the same but Qg the current is different.
Let three resistors connected irt parallel (as shown in fig) between the points A and B. Let V
be the p.d. across A and B. The current flowing through resistors are Ip I2 and I3 respectively.
V Current through R, l\ ~TT~ ...».(!)
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a
i
Current through
Current through
Total current, I = I, + I2 + I3
If R is the effective resistance Rp
(5)
• __ V
1
R2 """"
IV
,
+ R3
""""•
L ..........
(4)
(2)
(3)
and
v_ = _y_ _v_ _y_
If n equvalent resistors are connected in parallel, then,
1
n
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If n etjuvalent resistors are connected in series,
Current Internal Resistance and Terminal n.d. of a Cell
v
JWWVL
R
1=
R+r
Electricity
Distribution between e.ni.l and p.d.
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The resistance of the cell is called internal resistance. Resistance offered by the
electrolyte and electrode when current is drawn from the cells is called internal
resistance.
The value of internal resistance is low for a freshly prepared primary cell. When the cell is
put to more and more use, the value of internal resistance increases.
The value of internal resistance depends on
i. the surface area of the electrodes ii. the separation between the electrodes iii. the
nature of the electrodes and iv. the nature of the electrolyte
Terminal pd. of a cell is the p.d. between the terminals of the cell in a closed circuit.
Terminal p.d. is always less than the e.m.f. of the cell by an amount equal to the potential
drop across the internal resistance of the cell.
Let a cell of e.m.f E and internal resistance 'r' be connected across an external resistance R as
shown in fig,
e.m.f. of the cell = p.d. across R + p.d. across r. E = IR + Ir
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e.m.f
D.d.
i. It is the amount of
work done by a source
in taking a unit charge
once round the
complete circuit.
i. It is the amount of
work done in taking a
unit charge from one
point of a circuit to
another.
ii. It is a cause
ii. It is an effect
ill It is larger than the
Hi. It is always less
p.d. across any circuit than the e.m.f.
element
iv It is independent of the iv. P.d. between two
. external resistance in points is proportional
the circuit
to the resistance
V.
It is equal to the maxi- v. P.d. may exists bemum p.d. between the tween any two points
two terminals of
of a closed circuit.
asource when it is an
open circuit.
ui
Kirchhoff s Laws
I Law (Point Rule or Junction Rule) (statement of charge conservation principle)
The algebraic sum of the currents meeting at any junction in a closed circuit is zero.
ie.,
ie., At any junction in an electric circuit, total current entering the junction is equal to the
total current leaving the junction. II Law (Mesh Theorem or Loop Rule) (statement of
energy conservation'principle)
Terminal p.d. V = I, r
E-IR'+V
V = E-IR
e.mf(El
e.m.f is defined as the amount ofvlork done in ing unit electric charge once around a closed
circuit.
unit volt. (V)
A
f
B
D
'
r
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A/RiA
>
/i
.
1
C
In any closed loop, the algebraic sum of the products of the current and resistance of the
various branches of the loop are equal to the algebraic sum of the e.m.f. of the loop.
ZiR-ZE For the closed loop ABCD, itR, + ir = E
Current
For the closed loop DCFE, i,R,+ i2R, = 0 For the closed loop AEFBA, ir + i^ = E
Electricity
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Grouping of cells
Cells can be grouped or combined in three ways - > series, parallel and series cum parallel
(mixed grouping)
i. Series
,E,r E,r
o
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p'
R
D
Consider n cells, each of emf, E and internal III
resistance r are connected in series as shown in
K
the figure with an external resistance R. The -1 equivalent circuit is given below. 3*
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i.e., Effective e.m.f. = E = E
Total internal resistance = rp = —
m
Effective resistance = R + rp = R +—
m
Hence current,
1=
mE
T''
R+
R
vwwvwv
m
IfR»r,then R + — «
m
mR + r -Jl
"R
Effective e.m.f. = E
E + E ......... + E = nE
. + r = nr
Thus the current in the external resistance is same as the current due to a single cell.
Total internal resistance = rs = r + r + Effective resistance = R-»-rs =
IfR«r,then
r
r
i%
+ — « — , .'.I =m -
mm T
Hence current, I =
nE
R+nr
T
IfR»r,then I=n hr\KJ
Thus the current in the external resistance is n times the current due to a single cell.
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IfR«nr,then I = —
r
Thus the current in the external resistance is same as the current due to a single cell.
ie. maximum current can be drawn from the series combination of cells if the external
resistance is very high as compared to the internal resis- O tance of the cell S
U.
d
ii. Parallel $
Consider m cells each of e.m.f. E and internal resis- H
w tance 'r* are connected in parallel as shown in the 0
figure with an external resistance R. Being parallel, "> the effective e.m.f. is that of a
single cell.
Thus the current in the external resistance is m times the current due to a single cell.
ie. maximum current can be drawn from the parrallel combination of cells if the external
resistance is very low as compared to the internal resistance of the cell
iii. Mixed grouping-series cum parallel
In this case n cells each of e.m.f. *E' and internal resistance 'r' are co'nnected in series and
there are m such rows. This mixed group is then connected to an external resistance R.
Effective e.m.f. = Em = nE (emf is same being parallel)
sp
~ ,, nr Total internal resistance = r = —
sp
m
Effective resistance = R +r = R
p
—m
Hence current,
I=
nE
mnE
R+
nr I mR + nr
m
Current
The current in the circuit is maximum if mR + nr is minimum. For that
nr
m r
mR = nr or R = — or — = —. m
n R
Thus, current Imax =
mnE mE
or
2nr mnE 2mR
2r nE 2R
WHEATSTONE'S BRIDGE
E K,
In the Wheatstone's Bridge Network shown in the Fig. P,Q, R & S - Four resistances which
form a bridge
network.
G - Galvanometer of resistance G
E-Acell of e.m.f. 'E'
K, - Plug key and K2 - Tap key
Connections are made as shown in the above fig. Let M' be the current from the cell. When
the key K, is closed, according to Kirchhoff's junction rule, we have,
at A, i = i,+i2 atB,i,=i3+ig atD, i2+ig=i4 atC,i3 + i4 =i
(1)
According to mesh rule, we have, for the mesh ABDA, i,P + igG - i2R = 0 —— (2)
and for the mesh BCDB »
yj-i4S-ifG = 0 ——— (3) The value of the resistor 'S' is so adjusted that the galvanometer G
shows zero deflection. It means that no current is flowing through G. Then the bridge is said
to be balanced in this condition.
—— (4)
Electricity
i,Q .-. i,Q - i2S = 0
(7) [from eq. 5]
Hence i.P = LRand i.Q= LS
Then
i2 S
Ui (0
o
_P
Q
Jl
S
(8)
This is the Wheatstone's Bridge network equation.
METRE BRIDGE
0
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K
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-
AB
-
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- Acellofe.m.f. 'E'
- Plug Key
- Known resistance-Resistance box
- Unknown resistance (a wire)
- Galvanometer
Jockey
A uniform metallic wire of length one metre
Principle:
The Wheatstone's bridge balancing condition. Uses:
Metre bridge is used to find the value of unknown resistance, resistivity etc. Experiment:
Connections are made as shown in the Fig. Circuit is closed using K. A suitable resistance 'R'
is introduced in the resistance box. The jockey is moved along the wire AB and the position J
of the jockey for which galvanometer shows zero deflection is noted. Let AJ = / cm and BJ =
(100 - /) cm. Now the bridge is said to be balanced. Let 'r' be the resistance per cm of the
metre bridge wire. Then according to Wheatstone's bridge principle,
/.r ^X " (100-/)r~R
'•x= '*
100-/
Thus knowing R and /, the value of the unknown resistance X can be found out.
Then eq: (1), (2) & (3) take the form
i, = i, and i, = i. ——— (5)
- i2 R - 0
(6)
To find resistivity
* The diameter of the wire (X) is measured y. using a screw gauge. The radius is then
calculated. (A The area of cross section of the given wire is A =
«5 Ttr2- The length 'V of the wire is also measured using a metre scale. Then the resistivity of
the ma8
terial of the wire is jcr2X
Current Electricity
COMPARE THE E JMFS OF THE TWO CELLS.
(Q.m), can be found out.
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POTENTIOMETER * The slide - wire potentiometer was invented by y, Johann Christian
Poggendorff in 1841.
(/J Potentiometer is a device used for, measur- O ing p.d.
accurately, comparing e.m.fs of two cells, measuring internal resistance of a cell etc.
USES OF POTENTIOMETER
(i) Used to measure the emf of a cell accurately, (ii) Used to compare the emf of a cell
accurately, (iii) Used to measure current, resistance etc. (iv) Used to measure accurately the
potential difference between two points in an electric circuit.
Principle:
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A potentiometer consists of a number of segments of wire of uniform area of cross section
stretched on a wooden board between two thick copper stifips. Each segment of wire is 1 m
long. A lead acid accumulator, a key and a rheostat are connected between A and B. This
forms the primary circuit. The p.d to be measured is included in the secondary circuit (A cell,
galvanometer, high resistance and a jockey form secondary circuit).
Consider a current I flows from the primary circuit. Let p be the resistance per unit length of
the potentiometer wire.
The jockey is pressed at J where the galvanometer shows null deflection.
The p.d, across A and J = e.m.f. of the cell in the secondary cell.
E = Ip/ Eoc/
This shows that, a potentiometer works on the principle that when a steady current flows
through a wire of uniform cross section, the potential drop across any length of the wire is
directly proportional to that length.
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Cell of e.m.f, E
Plug Key
Rheostat
2 cells of e.m.fs E, and E2
Plug keys
Galvanometer
Jockey
Potentiometer wire Connections are made as shown in the Fig. Close the primary circuit.
Adjust the rheostat for a convenient current. Put the plug key K,, so that cell E, comes in the
circuit. Moving the jockey along the potentiometer wire find the position of the jockey for
which galvanometer shows zero deflection. Let /, be the balancing length. Thus by the
principle of
potentiometer, El oc /,
Similarly using plug key K2, note the balancing length /2 for the cell E2.
Then, E2 oc /2
E2 /2 The experiment is repeated by adjusting the
Ji rheostat. The average value of c is calculated.
INTERNAL RESISTANCE OF A CELL
R K2
LFRED
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Connections are made as shown in figure with key K^ open. Find the balancing length
/,
then E, oc /, —————— (1)
A suitable resistance R is introduced in the
secondary circuit, K» is closed. Now p.d. across
Current
Ris
ER
o
where r is the internal resistance. Find the cor-responding length /2. For this p.d.
Electricity
One kWh is also called Board of Trade Unit (BOT) or simply 'unit*.
Number of units of electricity consumed = Number
Watt x hour
R+r
,
oc/,
1000
(2)
note
. _ (2)
R
/2
Cft
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V2 We have, R = —- and Imax =
R
.
THERMAL EFFECTS OF CURRENT Electrical Energy and
Electric Power
Electrical energy is defined as the amount of work done in sending a current through a
conductor.
Electrical potver is defined as the rate of consumption of electrical energy ie., the rate at
which electrical energy is being converted into some other form.
Work done or energy, W = qV
W qV Power, P = — - —= VI ...... (1)
t
tv'
O Ul K
u. J
MM
S
p — - ..,<». y
A bulb of higher power, stronger current will flow. Hence higher wattage of bulb, smaller is
the resistance of the filament, (thick is the filament). If bulbs of different wattages are
connected in parallel, then highest wattage bulb will glow with maximum brightness.
(Parallel connection voltage is same).
( W2^
H=
R
W
Also P = I2R....... (2)
_V I
Q Ul
tt U.
P-T....... 0)
Unit -> S.I. unit of power is watt (W)
1 watt = 1 volt x 1 ampere or 1 joule/sec Power of an electric circuit is said to be 1 watt if
a current of 1 ampere flows through it for a p.d of 1
volt across its ends.
Note -> In mechanics the unit of power is often "horse power". 1 HP = 746 watt
Electrical energy, W = qV = Vlt = P x t
Ul « O
If the bulbs of different wattages are connected in series* the lowest power bulb will give
maximum brightness. (Series combination current is same, but resistance of the filament of
the bulb of lowest power is maximum ie., H = I2Rt)
Suppose we have 100 W - 220V bulb -» This implies that the bulb is used on a 220V.
Joules law of heating
Joules law of heating states that the amount of heat produced in a conductor when current
flows
through it is directly proportional to i. square of the current (I) flowing through the conductor.
ii. the resistance (R) of the conductor and iii. time (t) for which the current is passed.
ie., H = I2Rt joules
I2Rt 4.2
calorie
COMBINED LAWS
ie., Electrical energy = Electric power x time S.I. unit of electric energy is joule (J).
But for commercial purpose the unit is kilowatt hour. (kWh).
1 kWh = 1000 Wh = 1000 x 60 x 60 = 3.6 x 106J.
One kWh is the total energy consumed at the rate
of one kilowatt for one hour.
10
O
Ul
LL
W
O
Current Practical applications of heating effect of current
i. Fuse wire :
A fuse wire is a conducting alloy made of tin (63%) and lead (37%). It has a high resistance
and low melting point. It is always used in series with the electrical installations. It protects
the circuit from strong currents. When a high current flows, the fuse wire melts and breaks
the circuit. Thus it protects the external appliances from a serious damage. ii. Electric heater
and Electric iron :
Both are high power instruments. For a given
voltage P oc I, since H oc I2 hence heat produced due to current is high.
iii. Thermionic Emission :
When a metal is heated by passing electric current through it, it starts emitting electrons. This
phenomenon is called thermionic emission, (e.g. Electronic valve)
iv. The cable wires supplying current to an electric lamp are not practically heated while on
the other hand the filament of lamp becomes white hot
We know that H oc R . The lamp and cable
wires are in series. The resistance of the cable wires supplying the current to the lamp is very
small as compared to that of the filament of the lamp. Therefore more heating effect in the
filament of the lamp than that in the supply wires. Hence filament of lamp becomes white hot
white the wires remain practically unheated.
Electricity
Q UI DC ii.
UI »
o
Fig. 1
Current in the circuit, / =
E
R+r
Electric power,
P=I2R
a ui
UI
wo
o
iu
K u.
Efficiency of an electric device (n)
Efficiency of an electric device is defined as the ratio of its output powerto the input power
_ Output power Input power In the case of an electric motor,
Output mechanical power Input electric power
Inputpower-powerloss due to heat Input electric power
Efficiency of a battery or cell is maximum when its internal resistance is equal to
external resistance of the circuit.
Show Inattfae power output is maximum whenR=r.
UI (0
o
O UI
u.
dP n Power is maximum, when — = 0
This is possible only when R = r
E2 .-. Maximum power output = -7— watts
Thermoelectricity
The branch of electricity which deals with the generation of e.m.f. due to temperature
difference between various points of the same conductor or two different conductors in
contact with each other, is called as Thermoelectricity.
Thermoelectric effect was discovered by a Gertnan Physist, in 1821 and is also known as
Seebeck effect after his name.
The assembly of two different metals joined at their ends to have two junctions in a circuit is
called a thermocouple.
Seebeck Effect
The phenomenon of production of thermoelectric e,m.f. across the junctions of the
thermocouple due to difference of temperature at its two junctions is called Seebeck
effect or thermo-electric effect
The magnitude and direction of the e.m.f depends on the metals and the temperature
of the hot and cold junction.
Fe
UI W
o
Cold
Cu
Hot
B
Consider a battery of emf E and internal reistance r is , connected accross a pure
resistance of resistance R. Consider a Cu-pe thermocouple. A low resistance galvanometer G is connected in the circuit.
11
Electricity
Effect of temperature on thermo e.m.f.
Current
When the junction A is heated, and the other junction kept cold, the galvanometer shows
deflection. The direction of current in Cu - Fe thermocouple is jjj Consider a Cu - Fe
thermocouple from Cu to Fe through hot junction. fl£
Seebeck effect is reversible, ie., If the hot and Jj Yt cold junctions are interchanged the
direction of thermo J - electric current is reversed.
Thermo emf
The order of thermo emf is 10*v tolO~3V m Thermo emf is very small because, the rate of Q
change of junction potentials with temperature is very *H small. This is due to small change
in the number of force electrons per unit volume due to change of temperature.
Contact potential (Volta Effect) is the difference of potential when comes into
existance across the common interface when two different metals are placed in
contact with each other.
When two different metals are brought in contact, the free electrons tend to diffuse from the
metal with greater electron density to the other with lower free electron density. Due to this
diffusion contact potential is developed. This contact potential at two junctions remain the
same if two junctions are at same temperature. Hence no current flows. If one junction is
heated, rate of diffusion of free electrons at that junctions will change. Hence contact
potential of two junction become unequal. Hence effective p.d. called thermo e.m.f. is
developed
O Ul
a
u.
J
Ul
O
Temperature
If the temperature of cold junction is found that the thermo-emf increases uniformly with
temperature and reaches a maximum value at a particular
temperature called Neutral Temperature( 9n). As the temperature of the hotjunction increases
further the thermo-emf decreases and becomes zero and just reverse its direction of a
particular temperature called
temperature of inversion(9j)
ea-ec=ei-en •0 -e<+0i
* • o_ — ~"—- -' ——
Thermoelectric Series (Seebeck Series)
Thermoelectric series is a set of elements that can be used to build thermocouples. The series
is
Direction of current across hot junction^
Bi, Ni, Co, Pa, Pt, U, Cu, Mn, Ti, Hg, Pb, Sn, Cr,
M o. R h, Jt.A u,A g ,A /, Zn, Tn, Cd, Fe, As, Sb <————————————————-——
————— Direction of current across cold junction
For a given temperature difference, larger the gap between two elements forming
thermocouple, the greater will be the thermo e.m.f developed (order of millivolt). That is why
Sb - Bi couple gives maximum thermo emf (0.008V). The direction of thermo e.m.f or
current is from the first member to the second member in the series.
Certain alloys are used for making thermocouples.
e.g. At moderate temperature upto 260°C, Cu -Fe, iron - constantan (Cu & Ni alloy),
Cu - constan-tan are used. At high temperature upto 1650°C Pb -Pt(Pt-Rhodium) is
used.
O IM
THERMOELECTRIC POWER
Thermo e.m.f, 'E* of a Cu-Fe thermocouple varies with the temperature 9 of the hot junction. T
E=ct9+-p92
£*
where a and p are constants for a given pairs of elements forming a thermocouple.
d0
dE
Neutral temperature, 6n =
-a
UJ At inversion temperature, thermo emf becomes zero.
It 6 = 0 also
0 = 0{
2
S~ a# +_ p# - o
-
' 2
o
' Ul (ft .
/
1
\
aU+-
12
Current
e,
0 Ui
a: u.
Jt
UI
The rate of change of thermo emf with the change Jg in temperature of the hot junction is
called thermo- 0
electric power
dE d6
Temperature difference
D III
u.
i
iy O
Slope =
QR PR
Slope gives the value of p in the expression
K
^ = a + pe de
OA gives the value of' a '
PELTIER EFFECT
The liberation orabsorbation of heat at the junctions of a thermocouple due to the
pasage of an electric current is known as pettier effect
PELTIER COEFFICIENT
The rate of absorbtion or liberation of heat is directily
proportional to electric current
dH ie.
dt
ai
dH
. ..
— = jci or H = icit = nq, dt
where i - current, q - charge 1 TT' is called Pettier coefficient and its unit is J/C
Pettier coefficient is defined as the amount of heat liberated or absorbed at a junction when unit
current flows through it.
Peltiereffect -» H= rcit, i.e., H°ci Joule's effect -» H = i2Rt,' i.e., H °c i2
UI
Urn -J
i
Ul
o
•"*
Q III
tt LL
Electricity THOMSON EFFECT
In the year 1854, the Scottish scientist, William Thomson (later Lord Kelvin) discovered
that if a temperature difference exists between any two points of a conductor carrying
current, heat is either absorbed or liberated, depending on the material This is Thomson
effect Seebeck effect is the result of the combined effects of Peltier and Thomson.
If a charge 'q' is sent through a small section of
a conductor, having a temperature difference d6 between any two points, the quantity of heat
dH absorbed or liberated is
dHocqdG
i.e., dH = CTqd9, where CT is a constant known as Thomson coefficient for a given material
at a given temperature. CT can be +ve, -ve or zero.
If heat is absorbed when a current flows from the low temperature end (cold end) to high
temperature end (hot end) CT is +ve.
e.g. Cu, Ag, Zn, Sb, Cd etc.
If heat is absorbed when a current flows from hot end to cold end, CT is -ve.
e g. Fe, C o, M n, B i, Pt etc.
In the case of lead CT is
zero (almost).
DIFFERENCE BETWEEN JOULES EFFECT AND PELTIER EFFECT
Joule's heating effect
a. Always a heating effect. '
b. Rate of heat dissipated is directly proportional
dH .2
to the square of the current, i.e., — ^ i .
dt
c. Depends on the resistance of the conductor and takes place throughout the conductor.
d. Independent of the direction of the current. e. Irreversible effect. ' Peltier effect
i. There is absorption as well as liberation of heat atjunctions.
ii. Rate of heat absorbed or liberated at a junction is directly proportional to the
current, i.e.
dH
dt
cc I
O
iii. Depends on the nature of the materials and takes place only at the junction of the thermocouple.
iv. Depends on the direction of the current.
v. Reversible effect.
13
Current Applications of Thermoelectricity
i.
Thermopile : O
A thermophile is a sensitive instrument used for the jjj detection of heat radiation and its
intensity measure- y. ment. Seebeck effect is the working principle. «j|
It consists of large number of antimony - bismuth couples arranged in series. One set of
junctions is blackened and exposed to radiations while the other set of junctions is protected
from radiations. The thermo e.m.f. is measured using a sensitive galvanometer. The
instrument is calibrated to measure the intensity of heat radiation directly.
ii. Thermoelectric generator :
Thermocouple is used to generate electric power using Seebeck effect in remote areas. It can
be achieved by heating one junction in a flame of kero-sine oil lamp and keepingthe other
junction at room or atmospheric temperature. .The thermo e.m.f so developed is used to
operate radio recievers or even radio transmitters.
iii. Thermoelectric refrigerator :
The principle of thermoelectric refrigerator is Peltier
effect.
D III K U.
HI M O
Electricity
for both low and high temperature measurements. Copper- constantan thermocouple is
suitable at low temperature, upto 400 K. Platinum and Platinum-Rhodium alloy is suitable
upto 2000 K.
Wires of suitable materials are selected and ajunction (J) is formed. The wires are passed
through mica discs to keep them straight and without touching from each other. This
arrangement is kept inside a porcelain (or hard glass) tube. It is closed with a mica lid which
is fitted with two terminals T, and T2. The free ends of couple wires are connected to these
terminals. Before connecting to voltage measuring device, the terminals are connected to two
compensating leads L, and L2.
L
mica disc
Hot
UJ W O
:Cold
A calibration curve, similar to the one shown in Fig. is drawn by keeping the thermometer at
known temperatures and measuring the corresponding e.m.f s using a sensitive voltmeter.
If temperature of a bath is to be determined, the ther moelectric thermometer is placed in
contact with it. The value of e.m.f is measured. The temperature corresponding to this value
is then found out from the calibration graph.
N
Thermocouple can be constructed with semiconductors. Semiconductor thermocouples have
the advantage of higher thermoelectric power of the order of 1 milli volt/degree. With proper
semiconductor's cold junction temperature can £j be brought down to -809C. Heat can be exg tracted from the cooling chest of the refrigera- UL tor by keeping the cold junction of a
current — carrying thermocouple in contact with it. p»
i
O
temperature
X
iv .THERMOELECTRIC THERMOMETER $ Wide range, cheap, easily
accessible and Thermoelectric thermometer works on the 0 measurement of changing
temperature are the ad-principle of Seebeck effect. R
""* vantages.
Indirect measurement and different Thermoelectric thermometers can be used
cou les for different ran es m the
P
8
disadvantages.
14
A calibration curve, similar to the one shown in Fig. is drawn by keeping the thermometer at
known temperatures and measuring the corresponding e.m.f s using a sensitive voltmeter.
If temperature of a bath is to be determined, the ther moelectric thermometer is placed in
contact with it. The value of e.m.f is measured. The temperature corresponding to this value
is then found out from the calibration graph.
N
Thermocouple can be constructed with semiconductors. Semiconductor thermocouples have
the advantage of higher thermoelectric power of the order of 1 milli volt/degree. With proper
semiconductor's cold junction temperature can £j be brought down to -809C. Heat can be exg tracted from the cooling chest of the refrigera- UL tor by keeping the cold junction of a
current — carrying thermocouple in contact with it. p»
i
O
temperature
X
iv .THERMOELECTRIC THERMOMETER $ Wide range, cheap, easily
accessible and Thermoelectric thermometer works on the 0 measurement of changing
temperature are the ad-principle of Seebeck effect. R
""* vantages.
Indirect measurement and different Thermoelectric thermometers can be used
cou les for different ran es m the
P
8
disadvantages.
14