Download Electromagnetic Induction and Alternating Current

Electromagnetic Induction and Alternating Current
Unit IV: Electromagnetic Induction and Alternating Currents
Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy currents. Self and
mutual inductance.
Need for displacement current.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC
oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits, wattless current.
AC generator and transformer.
[1994]
Q.1
Q.2
Q.3
Explain why an ordinary moving coil ammeter used for dc can-not be sued to measure alternating
current?
You are given an air core coil, a bulb, an iron rod and a source of electricity, suggest a method to find
whether the given source is dc or ac. Explain your answer.
A student connects a long air core coil of manganin wire to 100 V d.c. source and records a current of
1.5 A. When the same coil is connected across a 100 V, 50 Hz ac source, the current reduces to 1.0 A.
(i)
Give reasons for this observation
(ii)
Calculate the value of reactance of the coil.
[1995]
Q.1
Q.2
A bar magnet falls from a height ‘h’ through a metal ring. Will its acceleration be equal to g? Give
reason for your answer ?
Sketch a graph showing variation of reactance of a capacitor with frequency of the applied voltage.
Xc
t
Q.3
Describe briefly the principle, construction and working of a transformer. Why is the cure laminated?
Q.4
A choke coil and a bulb are connected in series to an ac source. The bulb shines brightly. How does
the brightness change when an core is inserted in the choke coil?
[1996]
Q.1
Q.2
Q.3
Q.4
Prove that the power dissipated in an ideal resistor connected to an ac source is V2eff / R.
Prove that the energy stored in an inductor is ½ Li2, where L is inductance and i is current in the
inductor.
If a rate of change of 2 A/s induces an emf of 10 mV in a solenoid, what is the self-inductance of the
solenoid?
A capacitor, a resistor and a 40 mH inductor are connected in series to an ac source of frequency 60
Hz. Calculate the capacitance of the capacitor, if the current is in phase with the applied voltage.
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[1997]
Q.1
The electric current in the direction from B to A is decreasing. What is the direction of induced
current in the metallic loop kept above the wire as shown in fig.

 
A
Q.2
Q.3
Q.4
Q.5
B
Prove mathematically that he average power over a complete cycle of alternating current through an
ideal inductor is zero.
What is the power dissipated by an ideal inductor in ac circuit? Explain.
A radio frequency choke is air cored whereas an audio frequency choke is iron cored coil. Give reason
for this difference.
A sinusoidal voltage V = 200 sin 314 t is applied to a resistor of 10  resistance. Calculate
(i)
rms value of voltage
(ii)
rms value of current
(iii) Power dissipated as heat in watt.
[1998]
Q.1
What is the rms value of alternating current shown in fig.
2A
O
T
T/2
3T/2
t
-2A
Q.2
Q.3
Q.4
An ideal inductor is in turn put across 220 V, 50 Hz and 220 V, 100 Hz supplies. Will the current
flowing through it in the two cases be the same or different.
An electric lamp connected in series with a capacitor and an ac source is glowing with of certain
brightness. How does the brightness of the lamp change on reducing the capacitance?
The given fig. Shows an inductor L and resistor R connected in parallel to a battery through a switch
S, The resistance R is same as that of the coil that makes L. two identical bulbs P and Q are put in
each arm of the circuit as shown in fig. When S is closed, which of the two bulbs will light up earlier?
Justify your answer.
R
L
Q

B
S
B
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Q.5
Q.6
Q.7
How does the mutual inductance of a pair of coils change when (i) distance between the coils is
increased and (ii) number of turns in each coil is decreased? Justify your answer in each case.
An air coil solenoid is connected to an ac source and a bulb. If an iron core is inserted in the solenoid,
how does the brightness of the bulb change? Give reason for your answer.
When a capacitor is connected in series LR circuit, the alternating current flowing in the circuit
increases. Explain why?
[1999]
Q.1
Q.2
Q.3
What is the phase difference between the voltage across the inductance and capacitor in an ac circuit?
Show that Lenz’s law is in accordance with the law of conservation of energy.
Give the direction in which induced current flows in the wire loop, when the magnet moves towards
the loop as shown.
N
S
[2000]
Q.1
Q.2
If the number of turns in the solenoid is doubled, keeping other factors constant, how does the selfinductance of the coil change?
Fig. Shows two position of a loop PQR in a perpendicular uniform magnetic field. In which position
of the coil is there an induced emf?
○
○
P
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
○
R○
○
○
○
○
Q
P
○
○
○
○
Q
V
V
○
○
Q.3
Q.4
Q.5
R
○
(i)
○
○
○
○
○
○
○
(ii)
○
The instantaneous voltage from an ac source is given by E = 300 sin 314 t; what is the rms voltage of
the source.
The instantaneous current in an ac circuit is I = 0.5 sin 314 t, what is (i) rms value and (ii) frequency
of the current.



In the diagram given, a coil B is connected to low



voltage bulb L and placed parallel to another coil A as
 A  AC source
B
L


shown. Explain the following observations:

 


(a)
Bulb lights and


 
(b)
Bulb gets diameter if the coil B moves upwards.
~
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Q.6
X
Predict the direction of induce current in resistance R in fig. (a) and (b) given below. Given reason for
your answer.
R

Y
X1
R

Y1
X2
R

2
1
S
Y2
N
N
S
Q.7
A rectangular coil of N-turns and area of cross-sections A is held in a time varying magnetic field.
Deduce an expression for the emf induced in the coil.
Q.8 The instantaneous voltage from an ac source is given by V = 300 sin 314 t. What is the rms value of
the source?
Q.9 An a.c. source of frequency 50 Hz is connected to a 50 mH inductor and a bulb. The bulb glows with
some brightness. Calculate the capacitance of the capacitor to be connected in series with the circuit,
so that the bulb glows with maximum brightness.
Q.10 The output voltage of an ideal transformer connected to a 240 V ac mains is 24V. When this
transformer is used to light a bulb with rating 24V, 24 W. Calculate the current in primary coil of
circuit.
Q.11 What are eddy current? How they can be minimized? Give two applications of eddy currents.
[2001]
Q.1
Q.2
Q.3
Q.4
Q.5
What is the power dissipation in ac circuit in which voltage and current are given by
V = 300 sin (t + /2) I = 5 sin t
What are eddy currents? Give their one use.
A circular copper disc 10 cm in radius rotates at 20  rad/s about an axis through its center and
perpendicular to the disc. A uniform magnetic field of 0.2T acts perpendicular to the disc.
(i)
Calculate the potential difference developed between the axis of the disc and the rim.
(ii)
What is the induced current in the circuit whose terminals are connected between center of
disc and point of rim and the resistance of the circuit is 2.
In an ideal transformer, the number of turns in the primary and secondary are 200 and 1,000
respectively. If the power input to the primary is 10 kW at 200V. Calculate
(i)
output voltage and
(ii)
current in primary.
A bulb of resistance 10, connected to an inductor of inductance I, is in series with an ac source
marked 100V, 50 Hz. If the phase angle between the voltage and circuit is /4 radian, calculate the
value of L.
[2002]
Bulb
Q.1
An inductor L of reactance XL is connected in series with a bulb
B to an ac source as shown in fig. Explain briefly how does the
brightness of the bulb change when (i) number of turns of the
inductor is reduced and (ii) a capacitor of reactance XC = XL is
induced in the circuit.
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L


A.C. Source


AURORA CLASSES
Q.2
Q.3
Q.4
Q.5
Q.6
Q.7
What is meant by impedance? Give its unit. Using the phasor diagram or otherwise derive an
expression for the impedance of an ac circuit containing L, C and R in series. Find the expression for
resonant frequency.
An a.c. generator consists of a coil 100 turns and cross-sectional area of 3m2, rotating at an angular
frequency of 60 radians/second in a uniform magnetic field of 0.04 T. The resistance of the coil is 500
ohm. Calculate the (i) maximum current drawn from the generator and (ii) maximum power dissipated
in the coil.
If the rate of change of current 2 ampere/second induces an emf of 40 mV in the solenoid, what is the
self-inductance of this solenoid?
The closed loop PQR is moving into a uniform magnetic field acting at right angles to the plane of the
paper as shown. State?




 P
Q




















R




 S
If the self-inductance of an iron inductor increases from 0.01 mH to 10 mH on introducing the iron
core into it, what is the relative permeability of the core material used?
Twelve wires of equal length ‘l’ are connected to form a skeleton cube which moves with a velocity v
perpendicular to the magnetic field B. What will be the induced emf in each arm of the cube?
D
C
A
B

v
G
H
E
F
B
[2003]
Q.1
Q.2
Write S.I. unit of magnetic flux. Is it a scalar or a vector quantity?
How does the self-inductance of an air coil change, when (i) the number of turns in the coil is
decreased (ii) an iron rod is introduced in the coil.
[2004]
Q.1
Two circular coils, one of radius r and the other of radius R are placed co-axially with their centers
coinciding. For R > >r, obtain an expression for the mutual inductance of the arrangement.
R
 r
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C2
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C1
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Q.2
A uniform magnetic field exists normal to the plane of the paper over a small region of space. A
rectangular loop of wire is slowly moved with a uniform velocity across the field as shown. Draw the
graph showing the variation of (i) magnetic flux linked with the loop and (ii) the induced e.m.f. in the
loop with time.
    
    
     
    








   
   
   
   
b
Q.3
A bar magnet M is dropped so that it falls vertically through the coil C. The graph obtained for
voltage produced across the coil versus. Time is showing in figure (b).
(i)
Explain the shape of the graph.
(ii)
Why is the negative peak longer than the positive peak?
Magnet
V
Q.4
Q.5
Q.6
Q.7
R




Coil


C



Output
Voltage
In India Domestic power supply is at 220 V, 50 Hz; while in USA it is 110 V, 50 Hz. Give one
advantage and one disadvantage of 220 V supply over 110 supply.
A coil of inductance L, a capacitor of capacitance C and resistor of resistance R all put in series with
an alternating source of emd E = E0 sin t. Write expressions for (i) total impedance of circuit
(ii) frequency of source emf for which circuit will show resonance.
A circular coil of N-turns and radius R, is kept normal to a magnetic field, given by B = B0 cos t.
Deduce an expression for the emf induced in this coil. State the rule, which helps to detect the
direction of induced current.
What is induced emf? Write Faraday’s law of electromagnetic induction. Express it mathematically.
A conducting rod of length ‘’, with one end pivoted, is rotated with a uniform angular speed ‘’ in a
vertical plane, normal to a uniform magnetic field ‘B’, Deduce an expression for the emf induced in
this rod.
Q.8
Q.9
Derive an expression for (i) induced emf and (ii) induced current when a conductor of length ‘’ is
moved with a uniform velocity v, normal to a uniform magnetic field B. Assume the resistance of
conductor to be R.
A small piece of metal wire is dragged across the gap between the pole piece of a magnet in 0.5s. The
magnetic flux between the pole pieces is known to be 8  10-4 Wb. Estimate the induced emf in the
wire.
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Q.10 In a series RC circuit, R = 30, C = 0.25 F, V = 100 V and  = 1,00,000 rad/s. Find the current in
the circuit and calculate the voltage across the resistor and the capacitor.
Q.11 In the given circuit, the potential difference
L
R
across the inductor L and resistor R are 200 V

and 150V respectively and the r.m.s value of
current is 5A. Calculate (i) the impedance of the
circuit and (ii) the phase angle between the
voltage and the current.
[2005]
Q.1
Q.2
Q.3
Q.4
~
Explain with the help of a diagram, the principle and working of an a.c. generator? Write the
expression for the emf generated in the coil in terms of speed of rotation. Can the current produced by
an a.c. generator be measured with a moving coil galvanometer?
Define mutual inductance and gives its S.I. unit.
What is the power dissipated in an ac circuit in which voltage and current are given by
V = 230 sin (t + /2) and I = 10 sin t ?
What do you mean by mutual inductance of two nearby coils? Find an expression for mutual
inductance of a solenoid-coil system.
[2006]
Q.1
Q.2
Q.3
Q.4
.
Q.5
Q.6
The power factor of an ac circuit is 0.5. What will be the phase difference between voltage and current
in this circuit?
How is the mutual inductance of a pair of coils affect when
(i)
Separation between the coils is increased.
(ii)
The number of turns in each coils is increased.
(iii) A thin iron sheet is placed between the two coils, other factors remaining the same.
What are eddy currents? How are they produced? In what sense eddy currents are considered
undesirable in transformer? How they can be minimized? Give two applications of eddy currents.
A 0.5 m long metal rod PO completes the circuit as shown in the figure. T area of the circuit is
perpendicular to the magnetic field of flux density 0.15 T. If the resistance of the total circuit is3,
calculate the force needed to move the rod in the direction as indicated with a constant speed of 2ms-1.
× × ×
×
×
× Q×
× × ×
×
×
×
×
× × ×
×
×
×
×
× × ×
×
×
×
×
× × ×
×
×
×
P×
When an inductor L and a resistor R in series are connected across a 12 V, 50Hz supply, a current of
0.5A flows in the circuit. The current differs in phase from applied voltage by /3radian. Calculate the
value of R.
The primary coil of a ideal step up transformer has 100 turns and transformation ratio is also 100. The
input voltage and power are 220 V and 1100 W respectively. Calculate
(a)
the number of turns in the secondary.
(b)
The current in the primary.
(c)
The voltage across the secondary.
(d)
The current in the secondary.
(e)
The power in the secondary.
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[2007]
Q.1
Q.2
Q.3
Q.4
Q.5
Q.6
An electrical element X when connected to an alternating voltage source has a current through it
leading the voltage by /2 road. Identify X and write an expression for its reactance.
In a series LCR circuit, the voltage across an inductor, a capacitor and a resistor are 30V, 30 V and 60
V respectively. What is the phase difference between the applied voltage and the current in the
circuit?
Calculate the current drawn by the primary of a transformer which steps down 200 V to 20V to
operate a device of resistance 20. Assume the efficiency of the transformer to be 80%
OR
An a.c. voltage of 100 V, 50 Hz is connected across a 20-ohm resistor and 2mH inductor in series.
Calculate (i) impedance of the circuit, (ii) rms current in the circuit.
Explain the term ‘inductive reactance.’ Show graphically the variation of inductive reactance with
frequency of the applied alternating voltage.
An a.c. voltage E = E0 sin t 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 /2.
OR
Explain the term ‘capacitive reactance.’ Show graphically the variation of capacitive reactance with
frequency of the applied alternating voltage.
An a.c. voltage E = E0 sin t is applied across a pure inductor of capacitive C. Show mathematically
that the current flowing through it leads the applied voltage by a phase angle of /2.
An alternating current from a source is represented by
I = 10 sin 314 t
Write the corresponding values of
(i)
its ‘effective value’ and
(ii)
frequency of the source.
Explain with the help of a labeled diagram, the underlying principle and working of a step up
transformer. Why cannot such a device be used to step up dc voltage?
[2008]
Q.1
The instantaneous current and voltage of an a.c. circuit are given by
Q.2
I = 10 sin 300 t A and v = 200 sin 300 t V.
What is the power dissipation in the circuit?
The circuit arrangement given below shows that when an a.c.
passes through the coil A, the current starts flowing in the coil B.
(i)
State the underiying principle involved.
(ii)
Q.3
Mention two factors in which the current produced in the
coil B depends.









~
Coil A








~
Coil B
An a.c. source, generating a voltage v = vm sin t is connected to a capacitor of capacitance C. Find
the expression for the current, I flowing through it. Plot a graph of v and I versus t to show that the
current is /2shead of the voltage.
A resistor of 200 and a capacitor of 15.0 F are connected in series to a 220 V, 50 Hz a.c. source.
Calculate the current in the circuit and the rms voltage across the resistor and the capacitor. Is the
algebraic sum of these voltages more than the source voltage? If yes, resolve the paradox.
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Q.4
Q.5
Q.6
Q.7
Q.8
Or
Explain briefly, with the help of a labeled diagram, the basic principle of the working of an a.c.
generator.
In an a.c. generator, coil of N turn and area A is rotated at v revolutions per second in u uniform
magnetic file B. Write the expression for the emf produced.
A 100 turn coil area 0.1 m2 rotates at half revolution per second. It is placed in a magnetic field 0.01 T
perpendicular to the axis of rotation of the coil. Calculate the maximum voltage generated in the coil.
When current in a coil changes with time, how is the back emf induced in the coil related to it?
Two circular coils, one of radius r and the other of radius R are placed co-axially with their centers
coinciding. For R > > r, obtain an expression for the mutual inductance of the arrangement.
Prove that an ideal capacitor in an a.c. circuit does not dissipate power
If resistance of rod is R, what is the current induced in it
Derive expression for self-inductance of a long air-cored solenoid of length l, radius r and having
number of turns N.
A coil of number of terns N, area A is rotated at a constant angular speed , in a uniform magnetic
field B and connected to a resistor R. Deduce expression for:
(i)
Maximum emf induced in the coil.
(ii)
Power dissipation in the coil.
Q.10 Derive an expression for impedance of an a.c. circuit consisting of an inductor and a resistor.
Q.11 Draw a labelled circuit arrangement showing the windings of primary and secondary coil in a
transformer. Explain the underlying principle and working of a step up transformer.
Write any two major sources of energy loss in this device.
Q.12 A jet plane is traveling wrest at 450 ms-1. If the horizontal component of earth’s magnetic field at that
place is 4  10-4 T and the angle of dip is 30, find the emf induced between the ends of wings having
a span of 30 m.
Q.9
Q.13 An inductor 200 mH, capacitor 500  F, resistor 10 are connected in series with a 100 V, variable
frequency ac source. Calculate the
(i)
frequency at which the power factor of the circuit is unity
(ii)
current amplitude at this frequency.
(iii) Q-factor.
Q.14 An inductor of unknown value, a capacitor of 100  F and a resistor of 10 are connected in series to
a 200 V, 50 Hz a.c. source. It is found that the power factor of the circuit is unity. Calculate the
inductance of the inductor and current amplitude.
Q.15 How much current is drawn by the primary coil of a transformer which steps down 220 V to 22 V to
operate a device with an impedance of 220 .
[2009]
Q.1
(i)
(ii)
Q.2
(a)
State Faraday's law of electromagnetic induction.
A jet plane is travelling towards west at a speed of 1800 km/h. What is the voltage difference
developed between the ends of the wing having a span of 25 m, if the Earth's magnetic field at
the location has a magnitude of 5  10-4 T and the dip angle is 30°?
[3]
What are eddy currents? Write their two applications.
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(b)
(a)
(b)
Figure shows a rectangular conducting loop PQSR in which arm RS of length 'I' is movable.
The loop is kept in a uniform 'magnetic field 'B' directed downward perpendicular to the plane
of the loop. The arm RS is moved with a uniform speed 'v'.
Deduce an expression for
(i)
the emf induced across the arm 'RS',
(ii)
the external force required to move the arm, and
(iii)
the power dissipated as heat.
[5]
or
State Lenz's law. Give one example to illustrate this law. "The Lenz's law is a
consequence of the principle of conservation of energy."Justify this statement.
Deduce an expression for the mutual inductance of two long coaxial solenoids but having
different radii and different number of turns.
[5]
[2010]
Q.1
Q.2
Q.3
Define self-inductance of a coil. Write its S.I. units.
[1]
Two identical loops, one of copper and the other of aluminium, are rotated with the same angular
speed in the same magnetic field. Compare (i) the induced emf and (ii) the current produced in the two
coils. Justify your answer.
[2]
State Faraday’s law of electromagnetic induction.
Figure shows a rectangular conductor PQRS in which the conductor PQ is free to move in a uniform
magnetic field B perpendicular to the plane of the paper. The field extends from x = 0 to x = b and is
zero for x > b. Assume that only the arm PQ possesses resistance r. When the arm PQ is pulled
outward from x = 0 to x = 2b and is then moved backward to x = 0 with constant speed v, obtain the
expression for the flux and the induced emf. Sketch the variations of these quantities with distance 0 
x  2b.
S
P
Q
R
x=0
x=b
x=2b
Draw a schematic diagram of a step-up transformer. Explain its working principle. Deduce the
expression for the secondary to primary voltage in terms of the number of turns in the two coils. In an
ideal transformer, how is this ratio related to the currents in the two coils?
How is the transformer used in large scale transmission and distribution of electrical energy over long
distances?
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[2011]
Q.1
Two bar magnets are quickly moved towards a metallic loop connected across a capacitor ‘C’ as
shown in the figure. Predict the polarity of the capacitor.
[1]
C
S
Q.2
Q.3
N
S
N
What are eddy currents? Write any two applications of eddy currents.
[2]
State the working of a.c. generator with the help of a labeled diagram.
The coil of an a.c. generator having N turns, each of area A, is rotated with a constant angular
velocity . Deduce the expression for the alternating e.m.f. generated in the coil.
What is the source of energy generation in this device?
Or
(a)
Show that in a.c. circuit containing a pure inductor, the voltage is ahead of current by /2 in
phase.
(b)
A horizontal straight wire of length L extending from east to west is falling with speed v at
right angles to the horizontal component of Earth’s magnetic field B.
(i)
Write the expression for the instantaneous value of the e.m.f. induced in the wire.
(ii)
What is the direction of the e.m.f.?
(iii)
Which end of the wire is at the higher potential?
[2012]
Q.1
Q.2
Q.3
Q.4
Q.5
A bar magnet is moved in the direction indicated by the arrow between two coils PQ and CD. Predict
the direction of induced current in each coil.
[1]
Mention the two characteristic properties of the material suitable for making core of a transformer.
[1]
State the underlying principle of a transformer. How is the large scale transmission of electric energy
over long distances done with the use of transformers?
[2]
A light bulb is rated 200 W for 220 V ac supply of 50 Hz. Calculate
(i)
the resistance of the bulb;
(ii)
the rms current through the bulb.
[2]
OR
An alternating voltage given by V = 280 sin 50 t is connected across a pure resistor of 40 . Find
(i)
The frequency of the source.
(ii)
The rms current through the resistor.
A series LCR circuit is connected to an ac sourced. Using the phasor diagram, derive the expression
for the impedance of the circuit. Plot a graph to show the variation of current with frequency of the
source, explaining the nature of its variation.
[3]
[2013]
Q.1
Q.2
How does the mutual inductance of a pair of coils change when
(i)
distance between the coils is increased and
(ii)
number of turns in the coils is increased?
A rectangular conductor LMNO is placed in a uniform magnetic field of 0·5 T. The field is directed
perpendicular to the plane of the conductor. When the arm MN of length of 20 cm is moved towards
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left with a velocity of 10 ms-1, calculate the emf induced in the arm. Given the resistance of the arm to
be 5  (assuming that other arms are of negligible resistance) find the value of the current in the arm.
OR
A wheel with 8 metallic spokes each 50 cm long is rotated with a speed of 120 rev/min in a plane
normal to the "horizontal component of the Earth's magnetic field. The Earth's magnetic field at the
place is 0·4 G and the angle of dip is 60°. Calculate the emf induced between the axle and the rim of
the wheel. How will the value of emf be affected if the number of spokes were increased ?
Q.3
(a)
For a given a.c., i = im sin rot, show that the average power dissipated in a resistor R over a
complete cycle is 1/2 im2 R.
(b)
A light bulb is rated at 120W for a 240 V a.c. supply. Calculate the resistance of the bulb.
[2014]
Q.1
Define the term ‘mutual inductance’ between the two coils.
Obtain the expression for mutual inductance of a pair of long coaxial solenoids each of length  and
radii r1 and r2 (r2 > > r1). Total number of turns in the two solenoids are N1 and N2 respectively.
Q.2
A Voltage V = V0 sin t is applied to a series LCR circuit. Derive the expression for the average
power dissipated over a cycle.
Under what condition is (i) no power dissipated even though the current flows through the circuit, (ii)
maximum power dissipated in the circuit?
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SAMPLE PAPER
Q.1
Q.2
Q.3
State the phase relationship between the current flowing and the voltage applied in an ac circuit for
(i)
a pure resistor
(ii)
a pure inductor?
State the principle of an ac generator? Write an expression for the maximum emf produced in it?
A bulb B and a capacitor ‘C’ are connected in series to the a.c.
C
B
mains as shown in the given figure :
The bulb glows with some brightness. How will the glow of the
bulb change when a dielectric slab is introduced between the
plates of the capacitor? Give reasons in support of your answer?
Q.4
Q.5
Q.6
Mains
~
A small square loop, of side 2mm is placed inside and normal to the axis of a long solenoid. The
solenoid has a total of 2000 turns of wire uniformly wound over its total length of 2m. If the current
flowing in the solenoid wire changes from 1A to 3A in [ /100]th of a second, calculate the emf
induced in the square loop?
An LC circuit contains a 20mH inductor and a 50 F capacitor with an initial charge of 10mC. The
resistance of the circuit is negligible.
Assume the instant when circuit is closed to be t =0
(i)
what is the total energy stored initially?
(ii)
what is the frequency and time period of the LC oscillations?
(iii)
At what time is the energy stored?
The figure given below shows the variation of an alternating emf with time. What is the average value
of the emf for the shaded part of the graph?
e (volt)
314
0.
1
0.2
t(s
)
-314
Q.7
Name the phenomenon associated with the production of back emf in a coil due to change of electric
current through the coil itself?
Name and define the SI unit used for measuring this characteristic of the coil?
Q.8
Obtain an expression for the magnetic moment of an electron in a circular orbit of radius ‘r’ and
moving with a speed ‘v’. State the rule to find its direction. How does this magnetic moment change
when
(i)
(ii)
the frequency of revolution is doubled
the orbital radius is halved?
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Q.9
The give graphs (a) and (b) represent the variation of the opposition offered by the circuit element to
the flow of alternating current, with frequency of the applied emf. Identify the circuit element
corresponding to each graph.
Oppositio
n to
current
(a)
O
Frequen
cy
Oppositio
n to
current
Frequenc
y
A circuit is set up by connecting L= 100 mH, C =5 f and R =100 in series. An alternating emf of
(150 2) volt, (500/  ) Hz is applied across this series combination. Calculate the impedance of the
circuit. What is the average power dissipated in
(a)
the resistor
(b)
the capacitor
(c)
the indictor and
(d)
the complete circuit?
An electric lamp connected in series with a capacitor and an a.c. source is glowing with certain
brightness. How dose the brightness of the lamp change on reducing the capacitance?
A circular brass loop of radius ‘a’ and resistance ‘R’ is placed with its plane perpendicular to a
magnetic field which varies with time as B = B0 sin t. Obtain the expression for the induced current
in the loop?
An LC circuit contains a 20mH inductor and a 50 F capacitor with an initial charge of 10mC. The
resistance of the circuit is negligible.
Assume the instant when circuit is closed to be t = 0
(i)
What is the total energy stored initially?
(ii)
What is the frequency and time period of the LC oscillations?
(iii)
At what time is the energy stored?
a)
Completely electrical (i.e., stored in the capacitor)?
b)
Completely magnetic (i.e., stored in the inductor)?
State any rule, which relates the direction of electric current and the direction of the accompanying
magnetic field?
What is the phase difference between the voltage drop across ‘L’ and ‘C’ in a series LCR circuit
connected to an ac source?
Suppose you have two bars of identical dimensions one made of paramagnetic substance and the other
of diamagnetic substance. If you place these bars along a uniform magnetic field, show
diagrammatically, what modifications in the field pattern would take place in each case?
A magnetized needle in a uniform magnetic field experiences a torque but no net force. However, an
iron nail near a bar magnet experiences a force of attraction in addition to a torque? Explain?
(b)
Q.10
Q.11
Q.12
Q.13
Q.14
Q.15
Q.16
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B1
L
Q.17 Figure below shows an inductor ‘L’ and a resistor ‘R’ connected
in parallel to a battery through a switch. The resistance of ‘R’ is
the same as that of the coil that makes ‘L’. Two identical bulbs
are put in each arm of the circuit?
(i)
Which of the bulbs light up earlier when S closed?
(ii)
Will the bulbs be equally bright after sometime?
R
B2
S
Q.18 With the help of a labelled diagram explain the principle, constructions and working of an ac
generator?
Q.19 A current of 5 A is flowing through a 10 turn circular coil of radius 7 cm. The coil lies in the x –y
plane. What is the magnitude and direction of the magnitude and direction of the magnetic dipole
moment associated with it?
If this coil were to be placed in a uniform external magnetic field directed along the x –axis, in which
plane would the coil lie, when in equilibrium? (Take  = 22/7)
Q.20 A coil ‘when connected across a 10V dc supply’ draws a current of 2A. When it is connected across a
10V – 50Hz ac supply, the same coil draws a current of 1A. Explain why it draws lesser current in the
second case. Hence determine the self-inductance of the coil? (Take  =3)
Q.21 Name the SI unit of magnetic flux and show that it equals volt- sec. Give three possible ways of
producing an induced emf in a coil giving an example in each case. A copper loop and an aluminum
loop, incidental in shape and size, are removed form identical magnetic fields, from identical initial
positions, in equal time intervals. Compare the induced emf and currents produced in the two loops?
Q.22 Define angle of dip at a place. How does its value changes as one goes from magnetic pole to the
magnetic equator?
Q.23 Two identical bar magnet is ‘P’ and ‘Q’ are placed in two identical uniform magnetic fields as shown
in the figure. Justify that both the magnets are in equilibrium? Which one of these is in stable
equilibrium? Give reasons for your answer?
P
N
Q
S
S
N
Q.24 A rectangular coil ‘P’ is moved from a point ‘A’ to another point ‘B’ with uniform velocity ‘v’
through a region of a uniform magnetic field acting normally inwards as shown in the figure. Show
graphically
(i) the variation of magnetic flux associated with the coil with time.
(ii) variation of induced emf across points ‘X’ and ‘Y’ of the coil with time.
A
B
.
.
x x
x
Y
x x
x
Explain the nature of variation in magnetic flux as represented by the graph in first case?
x x
Q.25 Distinguish between the terms resistance and impedance of an a.c circuit. A capacitor ‘C’ and a
x x
resistor ‘R’ are connected in series in an ac circuit. Deduce, by drawing pharos diagram, a
mathematical expression for the impedance of this circuit. How will this impedance be affected when
the frequency of the applied signal is decreased and why?
X
P
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Q.26 In which direction will a freely suspended magnet align itself when placed at the magnetic pole of the
earth?
Q.27 An ac generator has a coil of ‘N’ turns each of area ‘A’, rotating with angular speed  in a uniform
magnetic field ‘B’,
(i)
What is the maximum emf between its slip rings?
(ii)
What is the flux associated with the coil when the emf across it is zero?
Q.28 A coil of n turns ‘and radius R’ carries a current ‘I’. It is unwound and rewound to make another coil
of radians ‘R/2’, current remaining the same. Calculate the ratio of the magnetic moments of the new
coil and the original coil?
What will be the effect on the interference fringes in Young’s double slit experiment when,
(i)
the monochromatic source is replaced by another monochromatic source of shorter
wavelength.
(ii)
monochromatic source is replaced by a source of white light. Justify your answer in
each case.
Q.29 A bar magnet is placed in a uniform magnetic field with its magnetic moment making an angle  with
the field. (i) Write an expression for the torque acting on the magnet and hence define its magnetic
moment (ii) Write an expression for the potential energy of the magnet in this orientation. Hence
obtain the orientation for which this energy becomes minimum?
Q.30 A small town with a demand of electric power 800kW at 200 V is situated 15km away from an
electric generating station. The resistance of the two wire line carrying power is 0.5 /km. The town
gets power from the line through a 4000W –220V step down transformer at a substation in the town?
(i) Estimate the line power losses in the form of heat
(ii) Assuming negligible power losses due to leakage, find the power that must be supplied by
the plant.
Q.31 A 50W –100 V electric bulb is to be used on a 200V –50Hz ac supply. Calculate the inductance of the
lamp so that it may glow with its normal brightness? (Take   3)
Q.32 A magnetic needle, free to rotate in a vertical plane, orients itself with its axis vertical at a certain
place on the earth. What are the values of
(a)
horizontal component of earth’s magnetic field.
(b)
angle of dip, at this place.
Q.33 When 100 V DC is applied across an inductor, a current of 1A flows through it. If the same inductor is
connected to a 100 V A.C. source, the current reduces to 0.5A. Why is the current reduced in the later
case? Calculate the value of the reactance of the inductor.
Q.34 A small town with a demand of 880 kw of electric power at 220 V is situated 15 Km away from an
electric plant generating power at 440 V. The resistance of the cable carrying power is 15 Ohm. The
town gets power through a 4400 – 220 V step down transformer at a sub-station in the town.
(a)
Calculate the line power loss in the from of heat.
(b)
How much power must the plant supply, assuming there is a negligible power loss due to
leakage?
(c)
Calculate the voltage drop in the line.
Q.35 Why does a metallic piece become very hot when it is surrounded by a coil carrying high frequency
alternating current?
Q.36 Give expression for the average value of the a c voltage
V = V0 Sin t
π
over the time interval t = 0 and t =
ω
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Q.37 Three students X, Y, and Z performed an experiment for studying the
variation of alternating currents with angular frequency in a series LCR
circuit and obtained the graphs shown below. They all used a.c. sources
of the same r. m. s. value and inductances of the same value.
What can we (qualitatively) conclude about the
(i)
capacitance value
(ii)
resistance values
used by them? In which case will the quality factor be maximum?
What can we conclude about nature of the impendence of the set up at frequency W0?
Q.38 A circular coil having 20 turns, each of radius 8 cm, is rotating about its vertical diameter with an
angular speed of 50 radian s-1 in a uniform horizontal magnetic field of magnitude 30 mT. Obtain the
maximum average and r. m. s. values of the emf induced in the coil.
If the coil forms a closed loop of resistance 10, how much power is dissipased as heat in it?
Q.39 A rectangular wire frame, shown below, is placed in a
uniform magnetic field directed upward and normal to
the plane of the paper. The part AB is connected to a
spring. The spring is stretched and released when the
wire A`B` has come to the position (t = 0). How would
the induced emf vary with time? Neglect damping.
Q.40 Figure shows two long cooxial solenoids, each of length
‘L’. The outer soleniod has an area of cross-section A and
number of turns length n1. The corresponding values for
the inner solenoid are A2 and n2. Write the expression for
self inductance L1, L2 of the two coils and their mutual
inductance M. Hence show that M< L1L2 .
Q.41 In the circuit shown below, R represents an electric bulb. If the
frequency of the supply is doubled, how should the values of C
and L be changed so that the glow in the bulb remains unchanged?
Q.42 With the help of a labelled diagram explain the principle? Construction and working of a step up
transformer? Why is the core of a transformer laminated?
Q.43 An inductor ‘L’, a capacitor ‘C’ and a resistors ‘R’ are connected in series in an a.c. circuit. Deduce,
with the help of suitable pharos diagrams, a mathematical expression for impedance of this circuit.
What is meant by resonance of this circuit? Prove that this circuit exhibits resonance at a frequency
give by 1/2 LC?
Q.44 The bulb glows with some brightness. How would the glow of the bulb change if an iron rod were
inserted in the coil? Give reasons in support of your answer.
Q.45 An air cored coil L and a bulb B are connected in series to the ac mains as shows in the given figure:
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Q.46 A magnet is being moved towards a coil with a uniform speed  as shown in the figure. State the
direction of the induced current in the resistor R.
[1]
Q.47 An athlete peddles a stationary tricycle whose pedals are attached to a coil having 100 turns each of
area 0.1m2. The coil, lying in the X-Y plane, is rotated, in this plane, at the rate of 50 rpm, about the
Y-axis, in a region where a uniform magnetic field, B = (0.01)kˆ tesla, is present. Find the
(i)
maximum emf
(ii)
average e.m.f
generated in the coil over one complete revolution.
Q.48
[2]
‘Box’ A, in the set up shown below, represents an electric device often used/needed to supply,
electric power from the (ac) mains, to a load.
It is known that Vo < Vi.
(a)
Identify the device A and draw its symbol.
[5]
(b)
Draw a schematic diagram of this electric device. Explain its principle and working. Obtain an
expression for the ratio between its output and input voltages.
(c)
Find the relation between the input and output currents of this device assuming it to be ideal.
Q.49 In India domestic power supply is 220V, 50Hz; while in USA it is 110V, 50Hz.Give one advantage
and one disadvantage of 220V supply over110 V supply.
[1]
Q.50 A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are
insulated from the core and carry a current of 2A. If the number of turns is 1000 per metre, Calculate
the magnetic intensity ‘H’ and the magnetic field ‘B’.
[2]
Q.51 The magnetic susceptibility for a specimen has a small negative value. To which class of the magnetic
substances, does the specimen belong? What is Meissner effect?
[2]
Q.52 A circular loop and a rectangular loop of wire are moving towards a uniform magnetic field region
from a field free space with a constant velocity ’v’ with their plane perpendicular to the magnetic
field. In which loop the induced emf is constant during the time of motion? What about the emf
induced in the other one?
[2]
Q.53 (a)
A simple A C generator having a constant magnetic field is connected to a resistive load.
Mention the reason for the effect of doubling the speed of rotation on the following.
(i)
Frequency of rotation
(ii)
the generated emf.
(b)
Obtain the frequency of a series L C circuit at resonance.
(c)
A person while walking through the doorway of a metal detector, it emits a sound. What does
it indicate? What is the underlying principle of metal detector?
[5]
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OR
(a)
Show diagrammatically two different arrangements used for winding the primary and
coils in a transformer.
secondary
(b)
Assuming the transformer to be an ideal one, write the expressions for the ratio of its output
voltage to input voltage.
(c)
The core of transformer is made of magnetic material. Give any two properties of such
materials used.
(d)
Write any four types of energy losses in transformer.
Q.54 Draw the magnetic field lines representing uniform magnetic field 5. Name and state the law, which
gives the direction of induced e.m.f. in electromagnetic induction.
Q.55 Draw a labelled diagram to explain the principle and working of an a.c. generator. Deduce the
expression for emf generated. Why cannot the current produced by an a.c. generator be measured with
a moving coil ammeter?
OR
Explain the principle, construction and working of a transformer. Mention any four causes of energy
loss in a transformer.
Q.56 An electric heater is connected, turn by turn, to a d.c. and a.c. sources of equal voltages. Will the rate
of heat production be same in the two cases? Explain.
Q.57 A resistor of resistance 400 , and a capacitor of reactance 200, are connected in series to a 220 V,
50 Hz, a.c. source. If the current in the current in the circuit is 0.49 ampere find the (i) voltage across
the resistor and capacitor (ii) value of inductance required so that voltage and current are in phase.
Q.58 A rectangular loop and a circular loop are moving out of a magnetic field to a field free region with a
constant velocity. It is given that the fields is normal to the plane of both the loops.
Draw the expected shaped of the graphs, showing the variation of the flux, with in both the cases.
What is the cause of the difference in the shape of the two graphs?
Q.59 How does the mutual inductance of pair of coils change, when (i) distance between the coils is
increased (ii) number of turns in each coils is decreased?
Q.60 A straight conductor PQ is moving in a uniform and time independent magnetic field as shown below.
Assuming that there is no loss of energy due to friction, deduce an expression for the power spent by
an external agency to move the arm PQ, with a constant speed v, in terms of the magnetic field, the
length PQ and speed v.
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Q.61 A long solenoid, with 20 turns per cm, has a small loop of area 4 cm2 placed inside the solenoid
normal to its axis. If the current carried by the solenoid changes steadily from 4A to 6A in 0.2 second,
what is the (average) induced emf in the loop while the currents is changing?
Q.62 A series LCR circuit is connected to an a-c source of voltage V and angular frequency . When only
the capacitor is removed, the current lags behind the voltage by a phase angle ‘’ and when only the
inductor is removed, the current leads the voltage by the same phase angle. Find the current flowing
and the average power dissipated in the LCR circuit.
Q.63 The motion of a copper plate is damped when it is allowed to oscillate between the pole pieces of a
magnet. State the cause of this damping.
Q.64 Two circular loops, of radii r and 2r, have currents I and I/2 flowing through them in clockwise and
anticlockwise sense respectively. If their equivalent magnetic moments are M1 and M2 respectively,
state the relation between M1 and M2 .
Q.65 An average induced emf of 0.4 V appears in a coil when the current in it is changed from 10 A in one
direction to 10A in opposite direction in 0.40 second. Find the coefficient of self induced of the coil.
Q.66 A conducting U tube can slide inside another U tube maintain electrical contact between the tubes.
The magnetic field is perpendicular to the plane of paper and is directed inward. Each tube moves
towards the other at a constant speed V. Find the magnitude of induced emf across the ends of the
tubes in terms of magnetic field B, velocity v and width of the tube.
Q.67 (a)
Out of the two arrangements, given below, for winding of primary and secondary coil in
transformer, which arrangement do you think will have higher efficiency and why?
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(b)
Show that, in a ideal transformer, when the voltage is stepped up by a certain factor, the
current gets stepped down by the same factor.
(c)
State any two causes of energy loss in a transformer.
OR
(a)
In a series LCR ac circuit, is the applied instantaneous voltage equal to the algebraic sum of
the
instantaneous voltages across the series elements of the circuit? Is the same true for r.m.s voltages?
(b)
Prove that in a series LCR circuit, the power dissipated depends not only on the voltage and
current but also on the cosine of the phase angle  between these two.
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