Mid Term Examination (2014-15) Physics (Set -A) Class: XII
1
Why is electrostatic potential constant throughout the volume of the conductor and has the
same value (as inside) on its surface?
Ans- Inside a conductor E=0, E =
, So V is constant.
1
½+½
2
A square coil, OPQR, of side a, carrying a current I, is placed
in the Y-Z plane as shown here. Find the magnetic moment
associated with this coil.
Ans- =Ia2̂
½+½
1
3
The susceptibility of a magnetic material is -0.085. Identify the magnetic type of material. A
specimen of this material is kept in a uniform magnetic field. Draw the modified field pattern.
Ans- Diamagnetic material ½
1
4
½
Current in a circuit falls steadily from 5.0 A to 0.0A in 100 ms. If an average e.m.f. of 200 V
is induced, calculate the self-inductance of the circuit.
Ans- e = - L
5
½
L= 4H
½
The instantaneous current and voltage of an ac circuit are a given by I = 10 sin314t A and
V = 50 sin (314t +) V. What is the power of dissipation in the circuit?
Ans- P=Vrms Irms cos φ
Φ=
6
7
8
1
1
½
P=0
½
Potentiometer wire, PQ of 1m length is connected to a
standard cell E1. Another cell, E2 of e.m.f. 1.02 V is
connected as shown in the circuit diagram with a resistance
‘r’ and a switch, S. When switch, S open, null position is
obtained at a distance of 51 cm from P. Calculate (i) potential
gradient of the potentiometer wire and (ii) e.m.f. of the cell
E1. (iii) When switch S is closed, will null point move towards P or towards Q? Give reason
for your answer.
i) K= 2 V/m
ii) E1=2 V
iii) No change
A long straight wire of a circular cross-section of radius ‘a’ carries a steady current ‘I’. The
current is uniformly distributed across the cross-section. Apply Ampere’s circuital law to
calculate the magnetic field at a point ‘r’ in the region for r < a.
Ans- Derivation 1
1
B=
What are eddy currents? How are these minimized in transformer?
Ans- Definition
1
By using laminated sheets of soft iron.
1
2
2
2
9
There is an inductor of 5 mH. Current flowing through the inductor at any instant of time is
given by the relation.
I = t2 + 4
If, ‘I’ is in ampere and ‘t’ in sec, find out (a) e.m.f. induced in the inductor at t=1s and t=3s
(b) plot e.m.f. v/s time graph.
Ans- (a) e = - L
E1 = 10-2 V, E2=3×10-2V
½ + ½ +1
(b)
2
10
The oscillating electric field of an electromagnetic wave is given by: Ey = 30 sin (2 × 1011t +
300π) Vm-1 (a) Obtain the value of the wavelength of the electromagnetic wave. (b) Write
down the expression for the oscillating magnetic field.
Ans- (a) λ=2/3 cm
1
(b) Bz = 10-7 sin (2 × 1011t + 300π) T
1
2
11
OR
How does a charge q oscillating at certain frequency produce electromagnetic waves? Sketch
a schematic diagram depicting electric and magnetic fields for an electromagnetic wave
propagating along the z-direction.
Ans- accelerating charge produces changing electric field and magnetic field.
1
Diagram 1
A series LCR circuit is connected to a variable frequency 230 V source. L = 5.0 H, C = 80µF,
R = 40 Ω.
Ans(a) Determine the source frequency which drives the circuit in resonance.
Ans-
3
50 rad/sec.
(b) Obtain the impedance of the circuit and the amplitude of current at the resonating
frequency.
Ans
+
40Ω, 8.1 A.
(c) Determine the rms potential drops across the three elements of the circuit. Show that the
potential drop across the LC combination is zero at the resonating frequency.
Ans1437.5V, 1437.5V, 230V
12
13
1
A slab of material of dielectric constant K has the same area as that of the plates of parallel
plate capacitor but has the thickness 2d/3, where d is the separation between the plates. Find
out the expression for its capacitance when the slab is inserted between the plates of the
capacitor. If the capacitance of a parallel plate capacitor increases from 3µF to 30µF by
inserting a dielectric slab in between its plates, then find the dielectric constant of the slab.
Ans- derivation 1
Expression 1
K= 10
1
A wire AB is carrying a steady current of 6A and is lying on the table. Another wire CD
carrying 4 A is held directly above AB at a height of 1mm. Find the mass per unit length of
3
3
14
the wire CD so that it remains suspended at its position when left free. Give the direction of
the current flowing in CD with respect to that in AB. (Take the value of g = 10 m/s2)
Ans- mass per unit length = 4.8×10-4 Kg/m
2
Direction of current is opposite
1
(a) For a given ac, i = im sin t, show that the average power dissipated in a resistor R over a
complete cycle is
Ans- Proof
15
16
17
18
3
R.
2
(b) A light bulb is rated at 125 W for a 250V ac supply. Calculate the resistance of the bulb.
Ans- R= 500 Ω
1
Explain the term ‘inductive reactance’. Show graphically the variation of inductive reactance
with frequency of the applied alternating voltage.
An ac voltage E=E0 sin is applied across a pure inductor of inductance L. Show
mathematically that the current flowing through it lags behind the applied voltage by a phase
angle of .
Ans- Explanation
½
Graph
½
Derivation
2
OR
Explain the term ‘capacitive reactance’. Show graphically the variation of capacitive
reactance with frequency of the applied alternating voltage.
An ac voltage E=E0 sin is applied across a capacitor of capacitance C. Show
mathematically that the current flowing through it leads the applied voltage by a phase angle
of .
Ans - Explanation
½
Graph
½
Derivation
2
A small compass needle of magnetic moment m is free to turn about an axis perpendicular to
the direction of uniform magnetic field B. The moment of inertia of the needle about the axis
is I. The needle is slightly disturbed from its stable position and then released. Prove that it
executes simple harmonic motion. Hence deduce the expression for its time period.
Ans- Derivation 1
Proof 1
Time period 1
A capacitor of unknown capacitance is connected across a battery of V volts. The charge
stored in it is 360 µC. When potential across the capacitor is reduced by 120 V, the charge
stored in it becomes 120 µC.
Calculate :(a) the potential V and the unknown capacitance C. (b) what will be the charge
stored in the capacitor, if the voltage applied had increased by 120 V?
Ans- (a) V= 180 V , C= 2µF
1+1
(b) 600 µC
1
Derive an expression for the electric field intensity, and electric potential, due to a short
electric dipole at a point on the equatorial line. Would the electric field be necessarily zero at
a point where the electric potential is zero? Give an example to illustrate your answer.
Ans- Diagram ½
Expression 1
Not necessary ½
Electric dipole mid point 1
3
3
3
3
19
State Kirchhoff’s rules of current distribution in an
electrical network. Using these rules determine the
value of the current I1 flowing in the circuit shown
in the figure.
Ans- AnsI3=I1+I2
20
21
22
23
24
3
5I1+2I2=2
1
-3I1+2I2=8
1
I1= A
Identify the following electromagnetic radiations as per the wavelengths given below. Write
one application each. (a) 102 m
(b) 10-2 m
(c) 1Å
Ans- (a) AM radio any one application
½+½
(b) Microwaves any one application
½+½
(c) X-rays any one application
½+½
A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What is
the area of the surface of water through which light from the bulb can emerge out? Refractive
index of water is 1.33. (consider the bulb to be a point source). Explain how does the
refraction of light affect the length of the day?
1
Ans- R= √
2
Area = 2.6 m
1
Explanation
1
By stating the sign convention and assumptions used, derive the relation between object
distance u, image distance v and focal length f for a concave mirror, when it forms a real
image of an object of finite size. Hence derive an expression for the linear magnification
produced.
Ans- Diagram
½
Derivation 1
Formula ½
Linear magnification 1
One day Rahul’s mother developed a severe stomach ache all of a sudden. She was rushed to
the doctor who suggested for an immediate endoscopy test and gave an estimate of
expenditure for the same. Rahul immediately contacted his class teacher and shared the
information with her. The class teacher arranged the money and rushed to the hospital. On
realizing that Rahul belonged to a below average income group family, even the doctor
offered concession for the test fee. The test was conducted successfully.
Answer the following questions based on the above information:
a) Which principle in optics is made use of in endoscopy?
Ans- total internal reflection.
2
b) Briefly explain the values reflected in the action taken by the teacher.
Ans- helpful, kind, concern
1
c) In what way do you appreciate the response of the doctor on the given situation?
Ans- love for his profession, kind
1
a) State the working principle of a potentiometer. With the help of the circuit diagram,
explain how a potentiometer is used to compare the e.m.f.’s of two primary cells. Obtain
the required expression used for comparing the e.m.f.’s.
Ans- principle
½
Circuit diagram 1
Expression
1½
b) Which material is used for potentiometer wire and why?
Ans- constantan, manganin because resistivity don’t change with temperature
½+½
c) How can the sensitivity of potentiometer be increased?
3
3
3
4
5
Ans- by increasing the length of the wire.
25
26
1
OR
a) Use Kirchhoff’s rules to obtain the balance condition in a Wheatstone bridge.
Ans- Diagram
½
Current distribution ½
Balancing condition 1
b) Draw a circuit diagram for determining the unknown resistance R using meter bridge.
Explain briefly its working , giving the necessary formula used.
Ans – circuit diagram ½
Working 1 ½
Formula
1
Explain with the help of a labeled diagram the working principle of a cyclotron. Show that
the cyclotron frequency does not depend on the speed of the particle. Write one of the uses
and point out one of the drawbacks of a cyclotron.
Ans- diagram 1
Working principle
2
Proof
1
Use
½
Drawback ½
OR
a)
A solenoid having 50 turns/cm, area of cross-section 1 cm2, has a core of a material with
relative permeability 400 and carry a current of 2A. Calculate magnetizing filed intensity
‘H’ magnetic dipole moment ‘M’ intensity of magnetization ‘I’ magnetic induction ‘B’
and magnetizing current ‘IM’.
Ans- H= 104A/m
½
2
M= 400 Am 1
I= 4 × 106A/m 1
B= 5.02 T 1
Im = 838 A ½
b)
Define magnetic equator.
Ans- Locus of all points on earth having zero angle of dip. 1
Draw a labeled diagram of an AC generator. Write the principle on which it works. Explain
how an alternating emf is generated with mathematical expression. An AC generator consists
of a coil 100 turns and cross-sectional area of 3 m2 rotating at a constant angular speed of 60
radian/sec in a uniform magnetic field of 0.04 T. The resistance of the coil is 500 ohm.
Calculate (a) maximum current drawn from the generator and (b) maximum power
dissipation in the coil.
AnsDiagram
Principle
Working
1
Mathematical expression 1
i) max. voltage = NBAω = 720 V
max. current = 1.44 A
1
ii) max. power = 518.4 W
1
OR
Derive an expression for the impedance of a series LCR circuit connected to an AC supply of
variable frequency.
Plot a graph showing variation of current with the frequency of the applied voltage. Explain
briefly how the phenomenon of resonance in the circuit can be used in the tuning mechanism
of radio or a TV set.
Ans: Phasor Diagram 1
Derivation 1
5
5
Expression 1
Graph 1
Explaination 1