Download Answer key of set B

ITL Public School
First - Term(2016-17)
Date: 19/09/16
Class: XII
Physics(042) Answer key
Time: 3hrs
1
2
M. M: 70
SECTION-A
An ac source of voltage V =V0 sin ωt is connected to an ideal capacitor. Draw graphs and phasor 1
diagram of voltage V and current I .
Ans. Graph
Phasor diagram
The variation of potential difference V with length l in case of
two
1
potentiometers wires P and Q is as shown. Which one of these
will you prefer
for comparing emfs of two primary cells and why?
Ans. Potentiometer Q
Smaller k = V/l, greater sensitivity
3
4
5
6
Define mobility of a charge carrier. How is the mobility affected with increase in temperature?
Ans. Definition
Mobility decreases
What is Meissner effect?
Ans. The perfect diamagnetic behaviour shown by super conductors.
Why alloys like constantan and manganin are used for making standard resistors.
Ans. (i) Resistance of alloys does not vary much with increase in temp.
(ii) High Resistivity, so even a smaller length of material
SECTION-B
1
1
1
Derive an expression for the energy stored in a parallel plate capacitor C, charged to a potential 2
difference V.
Ans. V =
dW = V dq = dq
W=∫
=∫
=
If V is the final potential difference between capacitor plates, then Q = CV
W=
7
8
=
= QV
The work is stored as Electrostatic potential energy, U = QV
(i) How are infrared waves produced? Write their one important use.
(ii) The thin Ozone layer on top of the stratosphere is crucial for human survival. Why?
Ans. (i) They are produced by hot bodies and molecules.
Any one use
(ii) It absorbs harmful UV rays
1
Find the charge on the capacitor as shown in the circuit.
Ans. Total resistance,
R = 10 + 20 = 30
The current, I =
A
Potential difference, V = IR =
10 =
2
2
Charge, q = CV = 6
9
= 4 μC.
Calculate the work done to dissociate the system of three charges
placed on the vertices of an equilateral triangle with each side equal to
10cm.
2
Ans. Potential energy of system i.e. work done to assemble the system
of charges
U=
(100 ) = -2.3
J
1
10
Work done to dissociate the system of charges
W = -U = 2.3
J
State Biot-Savart’s law. Using this law, find an expression for the magnetic field at the centre of a 2
circular coil of N-turns, radius r, carrying current I.
Ans. Statement
Figure
Derivation 1
SECTION-C
11
A thin metallic spherical shell of radius R carries a charge Q on its
surface. A point charge
is placed at the centre C and another
charge +2Q is placed outside the shell at A at a distance x from the
centre as shown in figure.
(i) Find the electric flux through the shell.
(ii) State the law used.
(iii) Find the force on the charge at the centre C of the shell and at
the point A.
Ans.(i) ϕ =
3
Total charge enclosed = Q + Q/2 = 3Q/2
ϕ = 3Q/2
(ii) Gauss law and statement
1
(iii)
12
13
=
1
Calculate the equivalent capacitance between points
A and B in the circuit below. If a battery of 10V is
connected across A and B, calculate the charge
drawn from the battery by the circuit.
Ans. =
3
This is the condition of balance so there will be no
current across PQ (50 F) 1
and are in series .
C12 = 200/3 = 20/3 F
C34 = 50/15 = 10/3 F
1
Equivalent capacitance between A and B = 20/3+10/3 = 10 F 1
A charge is distributed uniformly over a ring of radius ‘a’. Obtain an expression for the electric field 3
intensity E at a point on the axis of the ring. Hence show that for points at large distances from the
ring, it behaves like a point charge.
Ans. Figure
Derivation
Result E =
14
15
16
17
18
1
q/x2
1
Using Ampere’s circuital law, find an expression for the magnetic field at a point on the axis of a 3
long solenoid with closely wound turns.
Ans. Statement
Figure
Expression for B =
2
0nI
(i) When an AC source is connected to an ideal inductor show that
the average power supplied by the source over a complete cycle is
zero.
(ii) A lamp is connected in series with an inductor and an AC
source. What happens to the brightness of the lamp when the key is
plugged in and an iron rod is inserted inside the inductor? Explain.
Ans. (i) Pav = EI cosϕ
1
ϕ = /2
Pav = 0
1
(ii) L increases due to which current decreases and brightness also decreases.
3
1
Define the term mutual inductance. Consider two concentric circular coils, one of radius r 1 and the 3
other of radius r2 (r1< r2) placed coaxially which centres coinciding with each other. Obtain the
expression for the mutual inductance of the arrangement.
Ans. Definition
Figure
Derivation for expression
2
How are electromagnetic waves produced by oscillating charges?
3
Sketch a schematic diagram depicting electric and magnetic field for an electromagnetic wave
propagating in the Z-direction.
Ans. An oscillating charge produces an oscillating electric field in space, which produces an
oscillating magnetic field. These regenerate each other and this results in the production of EM
waves.
1
Diagram
2
OR
Write Maxwell’s generalization of Ampere’s Circuital Law. Show that in the process of charging a
capacitor, the current produced within the plates of the capacitor is
i = ε0
Where
is the electric flux produced during charging of the capacitor plates.
Ans. Amperes circuital law
1
∮ ⃗⃗⃗ ⃗⃗⃗ = μ0 Ic
Explanation
2
(i) With the help of a neat and labeled diagram, explain the principle and working of a moving coil 3
galvanometer.
(ii) What is the function of uniform radial field and how is it produced?
Ans. (i) Diagram
Principle
Working
1
(ii) Function of Uniform radial field – To have a linear scale
It is produced by having a magnet with concave pole pieces.
19
20
21
(i) Write the expression for the magnetic force acting on a charged
3
particle moving with velocity v in the presence of magnetic field
B.
(ii) A neutron, an electron and an alpha particle moving with equal
velocities, enter a uniform magnetic field going into the plane of
the paper as shown. Trace their paths in the field and justify your
answer.
⃗)
Ans. (i) = q (
1
(ii) Direction of force will be according to FLHR.
Figure
2
(i) Define the term drift velocity.
3
(ii) On the basis of electron drift, derive an expression for resistivity of a conductor in terms of
number density of free electrons and relaxation time. On what factors does resistivity of a conductor
depend?
Ans. (i) Definition
(ii) Derivation and Result
=
2
Factors affecting resistivity
Name the parts of the electromagnetic spectrum which is
3
(i) suitable for radar systems used in aircraft navigation.
(ii) used to treat muscular strain.
(iii) used as a diagnostic tool in medicine.
Write in brief, how these waves can be produced. Arrange these spectrums in the ascending order of
their wavelengths.
Ans. (i) Microwaves
(ii) Infrared
(iii) X rays
22
In ascending order X rays, IR and Microwaves
Method of production
1
A galvanometer of resistance G is converted into a voltmeter to measure upto V volts by connecting
a resistance R1 in series with the coil. If a resistance R2 is connected in series with it, then it can
measure upto V/2 volts. Find the resistance, in terms of R1 and R2, required to be connected to
convert it into a voltmeter that can read upto 2V. Also find the resistance G of the galvanometer in
terms of R1 and R2.
Ans. To measure V volts, V = Ig (G + R1)
3
V/2 volts, V/2 = Ig (G + R2)
2V volts, 2V = Ig (G + R3)
Solving, R3 = 3R1 – 2R2
23
1
SECTION-D
Ram is a student of class X in a village school. His uncle gifted him a bicycle with a dynamo fitted
in it. He was very excited to get it. While cycling during night, he could light the bulb and see the
objects on the road. He, however, did not know how this device works. He asked the question to his
teacher. The teacher considered it an opportunity to explain the working to the whole class.
(i)Write two values each displayed by Ram and his school teacher.
(ii)State the principle on which a dynamo works.
(iii)A circular coil of area 300 cm2 and 25 turns rotates about its vertical diameter with an angular
speed of 40 s-1 in a uniform horizontal magnetic field of magnitude 0.05 T. Obtain the maximum
voltage induced in the coil.
Ans. (i) Ram – Scientific aptitude, curiosity, positive approach
1
Teacher – Dedication, concern for students, motivational approach 1
4
(ii) Principle of dynamo/generator
(iii) E0 = NBAω
= 1.5 V
1
SECTION-E
24
(a) Draw a circuit diagram for a Wheatstone bridge. Use
Kirchoff’s rules to obtain the balance condition of the
Wheatstone bridge.
(b) In a meter bridge with R and S in the gaps, the null point
is found at 40 cm from A. If resistance of 30Ω is connected
in parallel with S, the null point at 50 cm from A. Determine
the values of R and S.
Ans.(a) Circuit diagram 1
Balance condition for a wheat stone bridge
(b) First case l1 = 40 cm
= =
and
Second case S/ = 30S/30+S
R/S| = 50/50 = 1
S| = R
Solving R = 10 Ω
S = 15Ω
5
1
1
OR
(a) Deduce the expression for the torque acting on a dipole of dipole moment placed in a uniform
electric field ⃗ . Depict the direction of the torque. Express it in the vector form.
(b) Show that the potential energy of a dipole making angle with the direction of the field is given
by u ( ) = - . ⃗ . Hence find out the amount of work done in rotating it from the position of
unstable equilibrium to the stable equilibrium.
Ans. (a) Fig
Expression and direction of torque 1
Vector form
(b) potential energy of a dipole, U = - p. E
Work done = - 2pE
25
1
1
(i) Draw a neat labeled diagram of a cyclotron.
(ii) Show that time period of ions in cyclotron is independent of both the speed of ion and radius of
circular path. What is the significance of this property?
(iii) An electron after being accelerated through a potential difference of 100 V enters a uniform
magnetic field of 0.004 T perpendicular to its direction of motion. Calculate the radius of the path
described by the electron.
Ans. (i) Diagram
(ii) T =
2
The applied voltage is adjusted so that the polarity of dees is reversed in same time that it
takes to complete one half of the revolution.
(iii) r = mv/qB = √
r = 8.4 X 10-3 m
/qB
1
1
5
26
OR
(i) Depict magnetic field lines due to two straight, long, parallel conductors carrying steady currents
I1 and I2 in the same direction.
(ii) Write the expression for the magnetic field produced by one of the conductor over the other.
Deduce an expression for the force per unit length.
(iii) Determine the direction of this force and define ampere.
(iv)Define the term magnetic inclination and horizontal component of Earth’s magnetic field at a
place. Establish the relationship between the two with the help of a diagram.
Ans. (i) Diagram
(ii) B = μ0 I1/2πr ;
f = F/L = μ0 I1I2/ 2πr N/m
2
(iii) Definition of ampere and direction of force
1
(iv) Definition of magnetic inclination and horizontal component of Earth’s field
1
H = B cos δ
(a) An ac source of voltage V = V0 sin ωt is connected to a series combination of L, C and R. Use
the phasor diagram to obtain expression for impedance of the circuit and phase angle between
voltage and current. Find the condition when current will be in phase with the voltage. What is the
circuit in this condition called?
(b) In a series LR circuit XL = R and power factor of the circuit P1. When capacitor with capacitance
C such that XL =XC is put in series, the power factor becomes P2. Calculate .
Ans. (a) Fig for LCR circuit
Phasor diagram
Expression for impedence Z and phase angle
Condition for resonance
1
(b) When XL = R
Z=√
=√
=√ R
1
P1 = cosϕ = R/Z = 1/√
When XL = XC, Z = R
P2 = R/Z = R/R = 1
P1/P2 = 1/√
OR
(i) Write the function of a transformer. State its principle of working with the help of a diagram.
Mention various energy losses in this device.
(ii) The primary coil of an ideal step-up transformer has 100 turns and transformation ratio is also
100. The input voltage and power are respectively 220V and 1100W. Calculate
(a) number of turns in secondary
(b) current in primary
(c) voltage across secondary
(d) current in secondary
(e) power in secondary
Ans. (i) Transformer converse low voltage ac high voltage ac and viceversa
Principle and diagram
1
Energy losses
1
(ii) (a) Ns = 10000
(b) Ip = 5 A
(c) Vs = 22000V
(d) Is = 0.05 A
(e) Ps = 1100 W
2
5
Answer key of set B
1
2
6
15
14
18
Two wires one of copper and other of manganin have same resistance and equal length. Which wire
is thicker and why?
Ans. Manganin wire is thicker because R = l/A. If is more, A should be larger for same
resistance.
An ac source of voltage V =V0 sin ωt is connected to an ideal inductor. Draw graphs and phasor
diagram of voltage V and current I .
Ans. Graph
Phasor diagram
Derive an expression for the electrostatic potential on the axial line of an electric dipole.
Ans. Figure
Derivation
1
(i) When an AC source is connected to an ideal capacitor, show that the
average power supplied by the source over a complete cycle is zero.
(ii) A lamp is connected in series with a variable capacitor and an AC
source. What happens to the brightness of the lamp when the key is
plugged in and capacitance of the capacitor is gradually reduced?
Ans. (i) Pav = EI cosϕ
ϕ = /2
Pav = 0
1
(ii) C increases due to which current decreases and brightness also decreases.
2
1
Figure
Expression for B =
2
0nI
Define the term self inductance. Derive an expression for self inductance of a long air-cored
solenoid of length ‘l’, cross-sectional area ‘a’ and having number of turns ‘N’.
Ans. Definition
2
1
3
Using Ampere’s circuital law. find an expression for the magnetic field due to a toroidal solenoid.
Ans. Statement
Figure
Derivation for expression
1
3
3