EMI

QUESTION FOR SHORT ANSWER

Q.1 Are induced emfs and currents different in any way from emfs and currents provided by a batteryconnected to a conducting loop?

Q.2 Can a charged particle at rest be set in motion by the action of a magnetic field? If not, why not? If so,how? Consider both static and time-varying fields.

Q.3 In Faraday’s law of induction, does the induced emf depend on the resistance of the circuit? If so, how?

Q.4 Figure shows a copper ring that is hung from a ceiling by two threads. Describe in detailhow you might most effectively use a bar magnet to get this ring to swingback and forth.

Q.5 Two conducting loops face each other a distance d apart, as shown in figure.An observer sights along their common axis from left to right. A clockwisecurrent i is suddenly established in the larger loop by a battery not shown. (a)What is the direction of the induced current in the smaller loop? (b) What isthe direction of the force (if any) that acts on thesmaller loop?

Q.6 A circular loop moves with constant velocity through regions where uniformmagnetic fields of the same magnitude are directed into or out of the planeof the page, as indicated in figure. At which of the seven indicated positionswill the induced current be (a) clockwise,(b) counterclockwise, and (c) zero?

Q.7 Can an induced current ever establish a magnetic field B

that is in the same direction as the magnetic fieldinducing the current? Justify your answer.

Q.8 A plane closed loop is placed in a uniform magnetic field. In what ways can the loop be moved withoutinducing an emf? Consider motions both of translation and rotation.

Q.9 Figure (a) shows a top view of the electron orbit in a betatron. Electrons are accelerated in a circular

orbit in the xy plane and then withdrawn to strike the target T. The magnetic field B

is along the z axis(the positive z axis is out of the page). The magnetic field Bz along this axis varies sinusoidally as shownin figure (b). Recall that the magnetic field must (i) guide the electrons in their circular path and (ii)generate the electric field that accelerates the electrons. Which quarter cycle(s) in figure are suitable (a)according to (i), (b) according to (ii), and (c) for operation of the betatron?

(a) (b)

Q.10(i) A piece of metal and a piece of non-metallic stone are dropped from the same height near the surface of

the earth. Which one will reach the ground earlier?

(ii) A metallic loop is placed in a nonuniform magnetic field. will an emf be induced in the loop ?

(iii) A wire loop is held with its plane horizontal. A magnet with its north pole downward is allowed to fallthrough it from some height. Will the magnet fall with constant acceleration? What will happen if the polesare reversed?

(iv) A magnet is dropped down into long vertically copper tube . Show that, even neglecting air resistancethe magnet will reach a constant terminal velocity .

(v) A magnet is dropped from the ceiling along the axis of a copper loop lying flat on the floor. If the fallingmagnet is photographed with a time sequence camera, what differences, if any will be noted if,(i) the loop is at room temperature (ii) the loop is packed in dry ice ?

Q.11 A copper ring is suspended in a vertical plane by a thread. A steel bar is passed through the ring in thehorizontal direction which is perpendicular to the plane of the loop. Then a magnet is similarly passedthrough the loop. Will the motion of the magnet and the bar affect the position of the ring?

Q.12 If the magnetic field outside a copper box is suddenly changed, what happens to the magnetic field insidethe box ? Such low-resistivity metals are used to form enclosures which shield objects inside themagainst varying magnetic fields.

Q.13 Metallic (nonferromagnetic) and nonmetallic particles in a solid waste may be separated as follows. Thewaste is allowed to slide down an incline over permanent magnets. The metallic particles slow down ascompared to the nonmetallic ones and hence are separated. Discuss the role of eddy currents in theprocess.

Q.14 A jet plane is flying due north . A potential difference is produced between he wing tips of the plane. Willa passenger sitting inside the plane also expect some emf between the wing tips? Will a tiny bulb connectedto the wing tips glow?

Q.15 Is the inductance per unit length for a solenoid near its centre ;(a) the same as(b) less than or (c) greater thanthe inductance per unit length near its ends ?

Q.16 Two solenoids A & B have the same diameter & length & contain only one layer of windings, withadjacent turns touching, insulation thickness being negligible . Solenoid A contains many turns of fine wire& solenoid B contains fewer turns of heavier wire.(i) which solenoid has the larger inductance ?(i) which solenoid has the larger inductive time constant ? (material is same)

Q.17 If the flux passing through each turn of a coil is the same, the inductance of the coil may be computed

from L = N

iB

. How might one compute L for a coil for which this assumption is not valid .

Q.18 If a current in a source of emf is in the direction of the emf, the energy of the source decreases, if a currentis in a direction opposite to the emf (as in charging a battery), the energy of the source increases . Dothese statements apply to the inductor .

Q.19 Does the time required for the current in particular LR circuit to build up to any given fraction of itsequilibrium value depend on the value of the applied emf .

Q.20 A steady current is set up in a coil with a very large inductive time constant . When the current isinterupted with a switch a heavy arc tends to appear at the switch blades . Explain? [Note : interruptingcurrents in highly inductive circuits can be dangerous]

Q.21 What is the advantage of placing the two electric wires carrying ac close together?

Q.22 In an LR series circuit the self induced emf is a maximum at the instant the switch is closed. How can thisbe since there is no current in the inductance at this instant .

Q.23 Explain what is meant by the statement “A motor acts as a motor and generator at the same time.” Canthe same be said for a generator?

Q.24 In a toroid, is the energy density larger near the inner radius or near the outer radius ?

Q.25 Two circular loops are placed with their centres separated by a fixed distance. How would you orientthe loops to have (a) the largest mutual inductance (b) the smallest mutual inductance ?

Q.26 If the resistance R in the left hand circuit of figure is increased, what is thedirection of the induced current in the right hand circuit ?

ONLY ONE OPTION IS CORRECT.Take approx. 2 minutes for answering each question.

Q.1 An electron is moving in a circular orbit of radius R with an angular acceleration . At the centre of theorbit is kept a conducting loop of radius r, (r <<R). The e.m.f induced in the smaller loop due to themotion of the electron is

(A) zero, since charge on electron in constant (B)

R4

er20

(C)

R4

er20 (D) none of these

Q.2 a conducting loop of radius R is present in a uniform magnetic field Bperpendicular the plane of the ring. If radius R varies as a function of time ‘t’, asR = R

0+ t. The e.m.f induced in the loop is

(A) 2(R0 + t)B clockwise (B) (R

0 + t)B clockwise

(C) 2(R0 + t)B anticlockwise (D) zero

Q.3 A wire loop is placed in a region of time varying magnetic field which is oriented orthogonally to the planeof the loop as shown in the figure. The graph shows the magnetic field variation as the function of time.Assume the positive emf is the one which drives a current in the clockwise direction and seen by theobserver in the direction of B. Which of the following graphs best represents the induced emf as afunction of time.

(A) (B) (C) (D)

Q.4 A square wire loop of 10.0 cm side lies at right angles to a uniformmagnetic field of 20T. A 10 V light bulb is in a series with the loop asshown in the fig. The magnetic field is decreasing steadily to zero over atime interval t. The bulb will shine with full brightness if t is equal to(A) 20 ms (B) 0.02 ms (C) 2 ms (D) 0.2 ms

Q.5 A long straight wire is parallel to one edge as in fig. If the current in the long wire is varies in time asI = I0e

–t/, what will be the induced emf in the loop?

(A) bI0 ln

d

ad(B)

2

bI0 ln

d

ad

(C) bI2 0 ln

d

ad(D)

bI0 ln

ad

d

Q.6 A rectangular loop with a sliding connector of length 10 cm is situated inuniform magnetic field perpendicular to plane of loop. The magneticinduction is 0.1 tesla and resistance of connector (R) is 1 ohm. Thesides AB and CD have resistances 2 ohm and 3 ohm respectively. Findthe current in the connector during its motion with constant velocity onemetre/sec.

(A) 110

1A (B)

220

1A (C)

55

1A (D)

440

1A

Q.7 The magnetic flux through a stationary loop with resistance R varies during interval of time T as = at(T – t). The heat generated during this time neglecting the inductance of loop will be

(A)R3

Ta 32

(B) R3

Ta 22

(C) R3

Ta2

(D) R

Ta 32

Q.8 The dimensions of permeability of free space can be given by(A) [MLT–2 A–2] (B) [MLA–2] (C) [ML–3 T2 A2] (D) [MLA–1]

Q.9 A wire as a parabola y = a x2 is located in a uniform magnetic field of inductance B, the vector B beingperpendicular to the plane xy. At the moment t = 0 a connector starts translation wise from the parabolaapex with a constant acceleration to find the emf of electromagnetic induction in the loop this formedas a function of y

(A) in = 2 Bya

2(B) in = By

a

2

(C) in = 2

By

a

2(D) in =

2

By

a

Q.10 A thin circular ring of area 10–2 m2 is held perpendicular to a uniform magnetic field of induction 0.1 T.A small cut is made in the ring and the galvanometer is connected across the ends such that the totalresistance of the circuit is 0.1 . The ring is squeezed to area 0.5 ×10–2 m2 in time 0.1 sec. The averageinduced current in the circuit is(A) insufficient data (B) 0.05 A (C) 0.5 A (D) 5 A

Q.11 A closed planar wire loop of area A and arbitrary shape is placed in a uniform magnetic field of magnitudeB, with its plane perpendicular to magnetic field. The resistance of the wire loop is R. The loop is nowturned upside down by 180° so that its plane again becomes perpendicular to the magnetic field. Thetotal charge that must have flowed through the wire ring in the process is(A) < AB/R (B) = AB/R (C) = 2AB/R (D) None

Q.12 A square coil ABCD is placed in x-y plane with its centre at origin. A longstraight wire, passing through origin, carries a current in negative z-direction.Current in this wire increases with time. The induced current in the coil is :(A) clockwise (B) anticlockwise(C) zero (D) alternating

Q.13 A vertical bar magnet is dropped from position on the axis of a fixed metalliccoil as shown in fig - I. In fig - II the magnet is fixed and horizontal coil isdropped. The acceleration of the magnet and coil are a1 and a2 respectivelythen(A) a1 > g , a2 > g (B) a1 > g , a2 < g (C) a1 < g , a2 < g (D) a1 < g , a2 > g fig - I fig-II

Q.14 Two identical coaxial circular loops carry a current i each circulating in the same direction. If the loopsapproach each other(A) the current in each will decrease (B) the current in each will increase(C) the current in each will remain the same(D) the current in one will increase and in other will decrease

Q.15 A long straight conductor is placed along axis of a circular coil of radius R. If the current,as shown in figure, starts decreasing with time, the current induced in loop would be(A) clockwise (ACB) (B) anticlockwise (ABC) (C) can not be decided (D) there will be no induced current.

Q.16 In a long hollow vertical metal pipe a magnet is dropped. During its fall, the acceleration of magnet:(A) will decrease linearly(B) will decrease upto a value which is less than g.(C) will decrease to zero and will attain a terminal speed(D) may increase or decrease

Q.17 In the arrangement shown in given figure current from A to B is increasing in magnitude. Induced currentin the loop will(A) have clockwise direction(B) have anticlockwise direction(C) be zero(D) oscillate between clockwise and anticlockwise

Q.18 An electric current i1 can flow either direction through loop (1) and inducedcurrent i2 in loop (2). Positive i1 is when current is from 'a' to 'b' in loop (1)and positive i2 is when the current is from 'c' to 'd' in loop (2)

In an experiment, the graph of i2 against time 't' is as shown below

Which one(s) of the following graphs could have caused i2 to behave as give above.

(A) (B)

(C) (D)

(E)

Q.19 A bar magnet is released from rest along the axis of a very long, vertical copper tube after some time, themagnet(A) will stop the tube (B) will move with almost constant speed(C) will move with acceleration g (D) will oscillate

Q.20 Figure shows a bar magnet and a long straight wire W, carrying current into theplane of paper. Point P is the point of intersection of axis of magnet and the lineof shortest distance between magnet and the wire. If P is the midpoint of themagnet, then which of the following statements is correct ?(A) magnet experiences a torque in clockwise direction (B) magnet experiences a torque in anticlockwise direction(C) magnet experiences a force, normal to the line of shortest distance(D) magnet experiences a force along the line of shortest distance

Q.21 A square coil ABCD is lying in xy plane with its centre at origin. A lng straightwire passing through origin carries a current i = 2t in negative z-direction. Theinduced current in the coil is(A) clockwise (B) anticlockwise (C) alternating (D) zero

Q.22 A negative charge is given to a nonconducting loop and the loop is rotated in theplane of paper about its centre as shown in figure. The magnetic field producedby the ring affects a small magnet placed above the ring in the same plane:(A) the magnet does not rotate (B) the magnet rotates clockwise as seen from below.(C) the magnet rotates anticlockwise as seen from below(D) no effect on magnet is there.

Q .23 Tw o infinitely long conducting parallel rails are connected through a capacitor C

as show n in the figure. A conductor of length l is moved with constant speedv

0.Which of the following graph truly depicts the variation of current

through the conductor with time ?

(A) (B)

(C) (D)

Q.24 Two identical conductors P and Q are placed on two frictionless rails R andS in a uniform magnetic field directed into the plane. If P is moved in thedirection shown in figure with a constant speed thenrod Q (A) will be attracted towards P(B) will be repelled away from P(C) will remain stationary(D) may be repelled or attracted towards P

Q.25 The figure shows an isosceles triangle wire frame with apex angle equal to /2. Theframe starts entering into the region of uniform magnetic field B with constant velocityv at t= 0. The longest side of the frame is perpendicular to the direction of velocity.If i is the instantaneous current through the frame then choose the alternative showingthe correct variation of i with time.

(A) (B) (C) (D)

Q.26 A thin wire of length 2m is perpendicular to the xy plane. It is moved with velocity s/m)kj3i2(v

through a region of magnetic induction 2m/Wb)j2i(B

. Then potential difference induced between

the ends of the wire :(A) 2 volts (B) 4 volts (C) 0 volts (D) none of these

Q.27 A long metal bar of 30 cm length is aligned along a north south line and moves eastward at a speed of 10ms–1. A uniform magnetic field of 4.0 T points vertically downwards. If the south end of the bar has apotential of 0 V, the induced potential at the north end of the bar is(A) + 12 V (B) – 12 V(C) 0 V (D) cannot be determined since there is not closed circuit

Q.28 A square metal loop of side 10 cm and resistance 1 is moved with a constantvelocity partly inside a magnetic field of 2 Wbm–2, directed into the paper, asshown in the figure. This loop is connected to a network of five resistors each ofvalue 3 . If a steady current of 1 mA flows in the loop, then the speed of theloop is(A) 0.5 cms–1 (B) 1 cms–1 (C) 2 cms–1 (D) 4 cms–1

Q.29 Two conducting rings P and Q of radii r and 2r rotate uniformly in oppositedirections with centre of mass velocities 2v and v respectively on aconducting surface S. There is a uniform magnetic field of magnitude Bperpendicular to the plane of the rings. The potential difference betweenthe highest points of the two rings is(A) zero (B) 4 Bvr (C) 8 Bvr (D) 16 Bvr

Q.30 Two coils, X and Y, are linked such that emf E is induced in Y when the current in X is changing at the rate

dt

dII . If a current I0 is now made to flow through Y, the flux linked with X will be

(A) EI0

I (B)

I

EI0 (C) (E

I ) I0 (D)

E

II0

Q.31 A conductor AB of length l oriented along x-axis moves in XY plane with velocity jivv 0

. AA

magnetic field jiBB 0

exists in the region. The induced emf is

(A) 2 B0lv0 (B) 2B0lv0 (C) B0lv0 (D) zero

Q.32 A conducting rod moves with constant velocity perpendicular to the long,straight wire carrying a current I as shown compute that the emf generatedbetween the ends of the rod.

(A) r

l

I0 (B)

r

l

2

I0 (C) r

l

I2 0 (D)

r

l

4

I0

Q.33 A conducting rod of length l moves with velocity a direction parallel to a long wire carrying a steadycurrent I. The axis of the rod is maintained perpendicular to the wire with near end a distance r away asshown in the fig. Find the emf induced in the rod.

(A) I0 ln

r

r l(B)

I2 0 ln

r

r l

(C) I0 ln

l

l

r(D)

2

I0 ln

r

r l

Q.34 A square loop of side a and resistance R is moved in the region of uniform magnetic field B(loopremaining completely insidefield) ,with a velocity v through a distance x . The work done is :

(A) R

vxB 2(B)

R

vxB2 22(C)

R

vxB4 22(D) none

Q.35 A metallic rod of length L and mass M is moving under the action of two unequal forces F1 and F2 (directedopposite to each other) acting at its ends along its length. Ignore gravity and any external magnetic field. Ifspecific charge of electrons is (e/m), then the potential difference between the ends of the rod is steady statemust be

(A) eMmLFF 21 (B) eMmL)FF( 21 (C) [ eMmL ] ln [F1/F2] (D) None

Q.36 Two parallel rigid wires are fixed at a distance ‘d’ apart, with each wire in a vertical position. The topends of the two wires are connected through an ideal inductor of inductance L. A straight connector ofmass M can slide freely up and down, maintaining electrical contact with the two wires, in a horizontalposition. A uniform magnetic field exists perpendicular to the plane of the wires. If the connector isreleased from rest, the graph of its downward velocity with time is :

(A) (B) (C) (D)

Q.37 A rod closing the circuit shown in figure moves along a U shaped wire at a constantspeed v under the action of the force F. The circuit is in a uniform magnetic fieldperpendicular to the plane. Calculate F if the rate of heat generation in the circuti is Q.

(A) F = Qv (B) F = v

Q(C) F = Q

v(D) F = Qv

Q.38 Two parallel long straight conductors lie on a smooth surface. Two other parallel conductors rest onthem at right angles so as to form a square of side a initially. A uniform magnetic field B exists at rightangles to the plane containing the conductors. They start moving out with a constant velocity v. If r is theresistance per unit length of the wire the current in the circuit will be

(A)r

Bv(B)

v

Br(C) Bvr (D) Bv

Q.39 There is a uniform magnetic field B normal to the xy plane. A conductor ABC has length AB = l1, parallelto the x-axis, and length BC = l2, parallel to the y-axis. ABC moves in the xy plane with velocity

jviv yx . The potential difference between A and C is proportional to

(A) vxl1 + vyl2 (B) vxl2 + vyl1(C) vxl2 – vyl1 (D) vxl1 – vyl2

Q.40 A conducting rod PQ of length 5 m oriented as shown in figure is moving with

velocity (2 m/s) i without any rotation in a uniform magnetic field )k4j3( Tesla.

Emf induced in the rod is(A) 32 Volts (B) 40 Volt (C) 50 Volt (D) none

Q.41 An equilateral triangular loop ADC of some finite magnetic field B

as shown inthe figure. At time t = 0, side DC of loop is at edge of the magnetic field. Magneticfield is perpendicular to the paper inwards (or perpendicular to the plane of the coil). The induced current versus time graph will be as

(A) (B) (C) (D)

Q.42 In the circuit shown in figure, a conducting wire HE is moved with a constantspeed V towards left. The complete circuit is placed in a uniform magnetic

field B

perpendicular to the plane of the circuit directed in inward direction.The current in HKDE is(A) clockwise (B) anticlockwise (C) alternating (D) zero

Q.43 The magnetic field in a region is given by B = B0 1F

HGIKJ

x

ak . A square loop of edge - length d is

placed with its edge along x & y axis. The loop is moved with constant velocity V V i 0

. The emf

induced in the loop is

(A)V B d

a0 0

2

(B) V B d

a0 0

2

2(C)

V B a

d0 0

2

(D) None

Q.44 When a ‘J’ shaped conducting rod is rotating in its own plane with constant

angular velocity w, about one of its end P, in a uniform magnetic field B

directed

normally into the plane of paper) then magnitude of emf induced across it will be

(A) B 22L l (B) 2LB2

1

(C) )L(B2

1 22 l (D) 2B2

1l

Q.45 A metal disc rotates freely, between the poles of a magnet in the directionindicated. Brushes P and Q make contact with the edge of the disc andthe metal axle.What current, if any, flows through R?(A) a current from P to Q (B) a current from Q to P(C) no current, because the emf in the disc is opposed by the back emf(D) no current, because the emf induced in one side of the disc is opposedby the emf induced in the other side.(E) no current, because no radial emf is induced in the disc

Q.46 For L-R circuit, the time constant is equal to(A) twice the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in theresistance(B) ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance(C) half the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in theresistance(D) square of the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in theresistance

Q.47 A rectangular coil of single turn, having area A, rotates in a uniform magnetic field B an angular velocity about an axis perpendicular to the field. If initially the plane of coil is perpendicular to the field, then theaverage induced e.m.f. when it has rotated through 90° is

(A)

BA(B)

2

BA(C)

4

BA(D)

BA2

Q.48 A ring of resistance 10, radius 10cm and 100 turns is rotated at a rate 100 revolutionsper second about a fixed axis which is perpendicular to a uniform magnetic field of induction 10mT. Theamplitude of the current in the loop will be nearly (Take : 2 = 10)(A) 200A (B) 2A (C) 0.002A (D) none of these

Q.49 A copper rod AB of length L, pivoted at one end A, rotates at constant angular velocity , at right anglesto a uniform magnetic field of induction B. The e.m.f developed between the mid point C of the rod andend B is

(A) 4

B 2l(B)

2

B 2l(C)

4

B3 2l(D)

8

B3 2l

Q.50 Figure shows a uniform magnetic field B confined to a cylindrical volume and is increasingat a constant rate. The instantaneous acceleration experienced by anelectron placed at P is (A) zero (B) towards right(C) towards left (D) upwards

Q.51 A triangular wire frame (each side = 2m) is placed in a region of time variant

magnetic field having dB/dt = 3 T/s. The magnetic field is perpendicular to theplane of the triangle. The base of the triangle AB has a resistance 1 while theother two sides have resistance 2 each. The magnitude of potential differencebetween the points A and B will be(A) 0.4 V (B) 0.6 V (C) 1.2 V (D) None

Q.52 In the adjoining circuit, initially the switch S is open. The switch ‘S’ is closedat t = 0. The difference between the maximum and minimum current thatcan flow in the circuit is(A) 2 Amp (B) 3 Amp(C) 1 Amp (D) nothing can be concluded

Q.53 The ratio of time constant in charging and discharging in thecircuit shown in figure is(A) 1 : 1 (B) 3 : 2(C) 2 : 3 (D) 1 : 3

Q.54 In an L-R circuit connected to a battery of constant e.m.f. E switch S is closed at time t = 0. If e denotesthe magnitude of induced e.m.f. across inductor and i the current in the circuite at any time t. Then whichof the following graphs shows the variation of e with i ?

(A) (B) (C) (D)

Q.55 A curren of 2A is increasing at a rate of 4 A/s through a coil of inductance 2H. The energy stored in theinductor per unit time is(A) 2 J/s (B) 1 J/s (C) 16 J/s (D) 4 J/s

Q.56 Two identical inductance carry currents that vary with time according to linearlaws (as shown in figure). In which of two inductance is the self induction emfgreater?(A) 1(B) 2(C) same(D) data are insufficient to decide

Q.57 The current in the given circuit is increasing with a rate a = 4 amp/s.The charge on the capacitor at an instant when the current in thecircuit is 2 amp will be :(A) 4C (B) 5C(C) 6C (D) none of these

Q.58 L, C and R represent physical quantities inductance, capacitance and resistance. The combination whichhas the dimensions of frequency is

(A)L

Rand

RC

1(B)

L

Rand

RC

1(C) LC (D)

L

C

Q.59 A coil of inductance 5H is joined to a cell of emf 6V through a resistance 10 at time t = 0. The emf

across the coil at time t = ln 2 s is:

(A) 3V (B) 1.5 V (C) 0.75 V (D) 4.5 V

Q.60 A long solenoid of N turns has a self inductance L and area of cross section A. When a current i flowsthrough the solenoid, the magnetic field inside it has magnitude B. The current i is equal to:(A) BAN/L (B) BANL (C) BN/AL (D) B/ANL

Q.61 A long straight wire of circular cross-section is made of a non-magnetic material. The wire is of radius a.The wire carries a current I which is uniformly ditributed over its cross-section. The energy stored perunit lenght in the magnetic field contained within the wire is

(A) U =

8

I20 (B) U =

16

I20 (C) U =

4

I20 (D) U =

2

I20

Q.62 The network shown in the figure is part of a complete circuit. If at acertain instant, the current I is 5A and it is decreasing at a rate of103 As–1 then VB–VA equals(A) 20 V (B) 15 V (C) 10 V (D) 5 V

Q.63 In Problem 62, if I is reversed in direction, then VB – VA equals(A) 5 V (B) 10 V (C) 15 V (D) 20 V

Q.64 Two resistors of 10 and 20 and an ideal inductor of 10 H are connected toa 2 V battery as shown. The key K is inserted at time t = 0. The initial (t = 0) andfinal (t ) currents through battery are

(A)15

1 A,

10

1 AA (B)

10

1 A,

15

1 AA

(C) 15

2 A,

10

1 AA (D)

15

1 A,

25

2 AA

Q.65 A small coil of radius r is placed at the centre of a large coil of radius R, where R >> r. The coils arecoplanar. The coefficient inductance between the coils is

(A) R2

r0(B)

R2

r20

(C) 2

20

R2

r(D) 2

0

R2

r

Q.66 Two long parallel wires whose centres are a distance d apart carry equal currents in opposite directions.If the flux within wires is neglected, the inductance of such arrangement of wire of length l and radius awill be

(A) L = l0 loge a

ad (B) L =

l0 loge a

d(C) L =

l0 loge d

a(D) none

Q.67 The inductor in a L–C oscillation has a maximum potential difference of 16 V and maximum energy of160 J. The value of capacitor in L–C circuit is(A) 0.8 F (B) 0.625 F (C) 1.6 F (D) 1.25 F

Q .68 In the circuit show n, the cell is ideal. The coil has an inductance of 4H and

zero resistance. F is a fuse of zero resistance and w ill blow w hen the current

through it reaches 5A . The sw itch is closed at t = 0. The fuse w ill blow :

(A ) just after t=0 (B ) after 2s

(C ) after 5s (D ) after 10s

Q.69 A coil of inductance L and zero resistance is connected to a source of variable emf at t = 0. The emf ofthe source is varied with time according to the graph shown on the right above. What will be the averagecurrent that flows through the coil during time T?(A) L2TV0 (B) L3TV0

(C) L2TV3 0 (D) LTV0

Q.70 In the LR circuit shown, what is the variation of the current I as a functionof time? The switch is closed at time t = 0 sec.

(A)

L

Rt

e1R

V(B) L

Rt

eR

V

(C) – LRt

eR

V (D) None

Q.71 In the circuit shown, X is joined to Y for a long time, and then X isjoined to Z. The total heat produced in R2 is :

(A) 21

2

R2

LE(B) 2

2

2

R2

LE(C)

21

2

RR2

LE(D) 2

1

22

R2

RLE

Q.72 An induction coil stores 32 joules of magnetic energy and dissipates energy as heat at the rate of 320watts. When a current of 4 amperes is passed through it. Find the time constant of the circuit when thecoil is joined across a battery.(A) 0.2 s (B) 0.1 s (C) 0.3 s (D) 0.4 s

Q.73 The figure shows a part of a complete circuit. The potentialdifference VB – VA when the current I is 5A and is decreasing ata rate of 103 As–1 is given by(A) 15 V (B) 10 V (C) –15 V (D) 20 V

Q.74 In a L–R decay circuit, the initial current at t = 0 is I. The total charge that has flown through the resistortill the energy in the inductor has reduced to one–fourth its initial value, is

(A) RIL (B) R2IL (C) R2IL (D) None

Q.75 A capacitor of capacitance 2 F is charged to a potential difference of 12 V. It is then connected acrossan inductor of inductance 0.6 mH. The current in the circuit when the potential difference across thecapacitor is 6 V is :(A) 3.6 A (B) 2.4 A (C) 1.2 A (D) 0.6 A

Q.76 In an LC circuit, the capacitor has maximum charge q0. The value of

di

dt max is

(A)q

LC0 (B)

q

LC0

(C)q

LC0 –1 (D) none of these

Q.77 An inductor coil stores U energy when i current is passed through it and dissipates energy at the rate of P.The time constant of the circuit, when this coil is connected across a battery of zero internal resistance is

(A) P

U4(B)

P

U(C)

P

U2(D)

U

P2

Q.78 The mutual inductance between the rectangular loop and the long straight wireas shown in figure is M.

(A) M = Zero (B) M =

b

c1ln

2

a0

(C) M =

b

caln

2

b0(D) M =

c

b1ln

2

a0

Q.79 A long straight wire is placed along the axis of a circular ring of radius R. The mutual inductance of thissystem is

(A) 2

R0 (B) 2

R0(C)

20 (D) 0

Q .80 The pow er factor of the circuit is 1/ 2 . The capacitance of the circuit is equal to(A) 400 F (B) 300 F(C) 500 F (D) 200 F

Q.81 An ac-circuit having supply voltage E consists of a resistor of resistance 3 andan inductor of reactance 4 as shown in the figure. The voltage across theinductor at t = T/2 is(A) 2 volts (B) 10 volts(C) zero (D) 4.8 volts

Q.82 In the circuit, as shown in the figure, if the value of R.M.S current is2.2 ampere, the power factor of the box is

(A) 2

1(B) 1

~

100 C

Box

1/ Henry

V = 220 volt, = 100 srms–1

(C) 2

3(D)

2

1

Q.83 When 100 V DC is applied across a solenoid a current of 1 A flows in it. When 100 V AC is appliedacross the same coil, the current drops to 0.5 A. If the frequency of the AC source is 50 Hz, theimpedance and inductance of the solenoid are:(A) 100, 0.93 H (B) 200, 1.0 H (C) 10, 0.86H (D) 200, 0.55 H

Q.84 An inductive circuit contains resistance of 10 and an inductance of 2.0 H. If an AC voltage of 120 Vand frequency 60 Hz is applied to this circuit, the current would be nearly:(A) 0.8 A (B) 0.48 A (C) 0.16 A (D) 0.32 A

Q.85 The power in ac circuit is given by P = ErmsIrmscos.The vale of cos in series LCR circuit at resonance is:

(A) zero (B) 1 (C) 2

1(D)

2

1

Q.86 In ac circuit when ac ammeter is connected it reads i current if a student uses dc ammeter in place of acammeter the reading in the dc ammeter will be:

(A) 2

i(B) 2 i (C) 0.637 i (D) zero

Q.87 In the circuti shown in the figure, R = C

L. Switch S is closed at time t = 0. The current throughC and

L would be equal after a time t equal to:(A) CR (B) CR ln (2)

(C) )2(lnR

L(D) LR

Q.88 In the circuit shown if the emf of source at an instant is 5 V, the potential differenceacross capacitor at the same instant is 4 V. The potential difference across R atthat instant can be

(A) 3V (B) 9V (C) 2

3V (D) none

Q.89 An AC current is given by I = I0 + I1 sin wt then its rms value will be

(A) 21

20 I5.0I (B) 2

02

0 I5.0I (C) 0 (D) 2I0

Q.90 Let f = 50 Hz, and C = 100 F in an AC circuit containing a capicator only. If the peak value of thecurrent in the circuit is 1.57 A at t = 0. The expression for the instantaneous voltage across the capacitorwill be(A) E = 50 sin (100 t – /2) (B) E = 100 sin (50 t)(C) E = 50 sin 100 t (D) E = 50 sin (100 t + /2)

Q.91 In a series CR circuit shown in figure, the applied voltage is 10 V and the voltage across capacitor isfound to be 8V. Then the voltage across R, and the phase difference between current and the appliedvoltage will respectively be

(A) 6V, tan–1

3

4(B) 3V, tan–1

4

3

(C) 6V, tan–1

3

5(D) none

Q.92 The phase difference between current and voltage in an AC circuit is /4 radian. If the frequency of ACis 50 Hz, then the phase difference is equivalent to the time difference :(A) 0.78 s (B) 15.7 ms (C) 0.25 s (D) 2.5 ms

Q.93 The given figure represents the phasor diagram of a series LCR circuitconnected to an ac source. At the instant t when the source voltageis given by V = V0cost, the current in the circuit will be (A) I = I0 cos(t + /6) (B) I = I0 cos(t – /6)(C) I = I0 cos(t + /3) (D) I = I0 cos(t – /3)

Q.94 A coil, a capacitor and an AC source of rms voltage 24 V are connected in series. By varying thefrequency of the source, a maximum rms current of 6A is observed. If coil is connected to a battery ofemf 12 volt and internal resistance 4, then current through it in steady state is(A) 2.4 A (B) 1.8 A (C) 1.5 A (D) 1.2 A

Q.95 Power factor of an L-R series circuit is 0.6 and that of a C–R series circuit is 0.5. If the element (L, C,and R) of the two circuits are joined in series the power factor of this circuit is found to be 1. The ratioof the resistance in the L-R circuit to the resistance in the C–R circuit is

(A) 6/5 (B) 5/6 (C) 33

4(D)

4

33

Q.96 The direct current which would give the same heating effect in an equalconstant resistance as the current shown in figure, i.e. the r.m.s. current,is

(A) zero (B) 2 A

(C) 2A (D) 2 2 AA

Q.97 The effective value of current i = 2 sin 100 t + 2 sin(100 t + 30°) is :

(A) 2 A (B) 322 (C) 4 (D) None

Q.98 In the circuit diagram shown, XC = 100 , XL = 200 andR = 100 . The effective current through the source is

(A) 2 A (B) 2 A

(C) 0.5 A (D) 22 A

Q.99 If I1, I2, I3 and I4 are the respective r.m.s. values of the time varying currents as shown in the four casesI, II, III and IV. Then identify the correct relations.

(A) I1 = I2 = I3 = I4 (B) I3 > I1 = I2 > I4 (C) I3 > I4 > I2 = I1 (D) I3 > I2 > I1 > I4

Q.100 In series LR circuit XL = 3R. Now a capacitor with XC = R is added in series. Ratio of new to old powerfactor is

(A) 1 (B) 2 (C) 2

1(D) 2

Q.101 The current I, potential difference VL across the inductor and potentialdifference VC across the capacitor in circuit as shown in the figure arebest represented vectorially as

(A) (B) (C) (D)

Q.102 A coil, a capacitor and an A.C. source of rms voltage 24 V are connected in series. By varying thefrequency of the source, a maximum rms current of 6 A is observed. If this coil is connected to a batteryof emf 12 V and internal resistance 4, the current through it will be(A) 2.4 A (B) 1.8 A (C) 1.5 A (D) 1.2 A

Q.103 In the shown AC circuit phase different between currents I1 and I2 is

(A)2

–tan–1

R

xL (B) tan–1

R

xx CL (C)2

+ tan–1

R

xL (D) tan–1

R

xx CL +2

Q.104 The circuit shown is in a uniform magnetic field that is into the page and isdecreasing in magnitude at the rate of 150 tesla/second. The ideal ammeterreads(A) 0.15 A (B) 0.35 A (C) 0.50 A (D) 0.65 A

Q.105 A capacitor C = 2F and an inductor with L = 10 H and coil resistance 5 are in series in a circuit.When an alternating current of r.m.s. value 2A flows in the circuit, the average power in watts in thecircuit is(A) 100 (B) 50 (C) 20 (D) 10

ONE OR MORE THAN ONE OPTION MAY BE CORRECTTake approx. 3 minutes for answering each question.

Q.1 The dimension of the ratio of magnetic flux and the resistance is equal to that of :(A) induced emf (B) charge (C) inductance (D) current

Question No. 2 to 5 (4 questions)The adjoining figure shows two different arrangements in which two square wire frames are placed in auniform constantly decreasing magnetic field B.

Q.2 The value of magnetic flux in each case is given by(A) Case I: = (L2 + 2)B; Case II: = (L2 – 2)B(B) Case I: = (L2 + 2)B; Case II: = (L2 + 2)B(C) Case I: = (L2 + 2)B; Case II: = (L2 – 2)B(D) Case I: = (L + )2B; Case II: = (L – )2B

Q.3 The direction of induced current in the case I is(A) from a to b and from c to d (B) from a to b and from f to e(C) from b to a and from d to c (D) from b to a and from e to f

Q.4 The direction of induced current in the case II is(A) from a to b and from c to d (B) from b to a and from f to e(C) from b to a and from c to d (D) from a to b and from d to c

Q.5 If I1 and I2 are the magnitudes of induced current in the cases I and II, respectively, then(A) I1 = I2 (B) I1 > I2 (C) I1 < I2 (D) nothing can be said

Q.6 Figure shown plane figure made of a conductor located in a magneticfield along the inward normal to the plane of the figure. The magneticfield starts diminishing. Then the induced current(A) at point P is clockwise(B) at point Q is anticlockwise(C) at point Q is clockwise(D) at point R is zero

Q.7 A conducting wire frame is placed in a magnetic field which is directed into thepaper. The magnetic field is increasing at a constant rate. Thedirections of induced currents in wires AB and CD are(A) B to A and D to C (B) A to B and C to D(C) A to B and D to C (D) B to A and C to D

Q.8 Two circular coils A and B are facing each other as shown in figure.The current i through A can be altered(A) there will be repulsion between A and B if i is increased (B) there will be attraction between A and B if i is increased(C) there will be neither attraction nor repulsion when i is changed(D) attraction or repulsion between A and B depends on the direction of current. It does not depend whether the current is increased or decreased.

Q.9 When a magnet with its magnetic moment along the axis of a circular coil and directed towards the coilis withdrawn away from the coil, parallel to itself, the current in the coil, as seen by the withdrawingmagnet is(A) zero (B) clockwise(C) anticlockwise (D) independent of the resistance of the coil

Q.10 A bar magnet is moved along the axis of copper ring placed far away from the magnet. Looking from theside of the magnet, an anticlockwise current is found to be induced in the ring. Which of the followingmay be true?(A) The south pole faces the ring and the magnet moves towards it.(B) The north pole faces the ring and the magnet moves towards it.(C) The south pole faces the ring and the magnet moves away from it.(D) The north pole faces the ring and the magnet moves away from it.

Q.11 In previous question, if P is on the left of midpoint :(A) magnet experiences no torque(B) magnet experiences no net force but experiences a torque(C) magnet experiences a rightward force as well as a torque(D) magnet will not experiences a rightward force as well as a torque

Q.12 Two circular coils P & Q are fixed coaxially & carry currents I1 and I2 respectively(A) if I2 = 0 & P moves towards Q, a current in the samedirection as I1is induced in Q(B) if I1 = 0 & Q moves towards P, a current in the opposite direction tothat of I2 isinduced in P.(C) when I1 0 and I2 0 are in the same direction then the two coils tend to move apart .(D) when I1 0 and I2 0 are in opposite directions then the coils tends to move apart.

Q.13 AB and CD are smooth parallel rails, separated by a distance l, andinclined to the horizontal at an angle . A uniform magnetic field ofmagnitude B, directed vertically upwards, exists in the region. EF is aconductor of mass m, carrying a current i. For EF to be in equilibrium,(A) i must flow from E to F (B) Bil = mg tan (C) Bil = mg sin (D) Bil = mg

Q.14 In the previous question, if B is normal to the plane of the rails(A) Bil = mg tan (B) Bil = mg sin (C) Bil = mg cos (D) equilibrium cannot be reached

Q.15 A conducting rod PQ of length L = 1.0 m is moving with a uniform speedv = 20 m/s in a uniform magnetic field B = 4.0 T directed into the paper.A capacitor of capacity C = 10 F is connected as shown in figure. Then (A) qA = + 800C and qB = – 800C(B) qA = – 800C and qB = + 800C(C) qA = 0 = qB(D) charged stored in the capacitor increases exponentially with time

Q.16 The e.m.f. induced in a coil of wire, which is rotating in a magnetic field, does not depend on(A) the angular speed of rotation (B) the area of the coil(C) the number of turns on the coil (D) the resistance of the coil

Q.17 A semicircle conducting ring of radius R is placed in the xy plane, as shown in the figure. A uniformmagnetic field is set up along the x–axis. No emf, will be induced in the ring. if

(A) it moves along the x–axis (B) it moves along the y–axis(C) it moves along the z-axis (D) it remains stationary

Question No. 18 to 20 (3 questions)A conducting ring of radius a is rotated about a point O on its periphery asshown in the figure in a plane perpendicular to uniform magnetic field Bwhich exists everywhere. The rotational velocity is .

Q.18 Choose the correct statement(s) related to the potential of the points P, Q and R(A) VP – VO > 0 and VR – VO < 0 (B) VP = VR > VO(C) VO > VP = VQ (D) VQ – VP = VP – VO

Q.19 Choose the correct statement(s) related to the magnitude of potential differences

(A) VP – VO = 2

1Ba2 (B) VP – VQ =

2

1Ba2

(C) VQ – VO = 2Ba2 (D) VP – VR = 2Ba2

Q.20 Choose the correct statement(s) related to the induced current in the ring(A) Current flows from Q P RQ(B) Current flows from Q R Q(C) Current flows from Q P and from QRO(D) No current flows

Q.21 Current growth in two L-R circuits (b) and (c) as shown in figure (a). Let L1, L2, R1 and R2 be thecorresponding values in two circuits. Then(A) R1 > R2 (B) R1 = R2 (C) L1 > L2 (D) L1 < L2

t

(b) (c)

i

(a) (b) (c)Q.22 A circuit consisting of a constant e.m.f. 'E', a self induction 'L' and a

resistance 'R' is closed at t = 0. The relation between the current Iin the circuit and time t is as shown by curve 'a' in the fig. When oneor more of parameters E, R & L are changed , the curve 'b' is obtained.The steady state current is same in both thecases. Thenit is possible that : (A) E & R are kept constant & L is increased(B) E & R are kept constant & L is decreased(C) E & R are both halved and L is kept constant(D) E & L are kept constant and R is decreased

Q.23 A circuit element is placed in a closed box. At time t=0, constant currentgenerator supplying a current of 1 amp, is connected across the box.Potential difference across the box varies according to graph shown infigure. The element in the box is :(A) resistance of 2 (B) battery of emf 6V(C) inductance of 2H (D) capacitance of 0.5F

Q.24 A constant current i is maintained in a solenoid. Which of the following quantities will increase if an ironrod is inserted in the solenoid along its axis?(A) magnetic field at the centre. (B) magnetic flux linked with the solenoid(C) self-inductance of the solenoid (D) rate of Joule heating.

Q.25 The symbols L, C, R represent inductance, capacitance and resistance respectively. Dimension offrequency are given by the combination

(A) 1 / RC (B) R / L (C)LC

1(D) C / L

Q.26 An LR circuit with a battery is connected at t = 0. Which of the following quantities is not zero just afterthe circuit(A) current in the circuit (B) magnetic field energy in the inductor(C) power delivered by the battery (D) emf induced in the inductor

Q.27 The switches in figures (a) and (b) areclosed at t = 0(A) The charge on C just after t = 0 is EC.(B) The charge on C long after t = 0 is EC.(C) The current in L just after t = 0 is E/R.(D) The current in L long after t = 0 is E/R.

Q.28 At a moment (t = 0) when charge on capacitor C1 is zero, the switch is closed. If I0 be the currentthrough inductor at that instant, for t > 0,(A) maximum current through inductor equals I0/2.

(B) maximum current through inductor equals 21

01

CC

IC

(C) maximum charge on C1 =21

101

CC

LCIC

(D) maximum charge on C1 = I0C121 CC

L

Q.29 For L – R circuit, the time constant is equal to

(A) twice the ratio of the energy stored in the magnetic field to the rate of the dissipation of energy in theresistance.(B) the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in the resistance.(C) half of the ratio of the energy stored in the magnetic field to the rate of dissipation of energy in theresistance.(D) square of the ratio of the energy stored in the magnetic field to the rate of dissipation energy in theresistance.

Q.30 An inductor L, a resistance R and two identical bulbs B1 and B

2 are

connected to a battery through a switch S as shown in the figure. Theresistance of coil having inductance L is also R. Which of the following statement gives the correct description of the happenings when the switch S is closed?(A) The bulb B

2 lights up earlier than B

1 and finally both the bulbs shine equally bright.

(B) B1 light up earlier and finally both the bulbs acquire equal brightness.

(C) B2 lights up earlier and finally B

1 shines brighter than B

2.

(D) B1 and B

2 light up together with equal brightness all the time.

Q.31 Which of the following quantities can be written in SI units in Kgm2A–2S–3?(A) Resistance (B) Inductance (C) Capacitance (D) Magnetic flux

Q.32 In figure, the switch S is closed so that a current flows in the iron-core inductorwhich has inductance L and the resistance R. When the switch is opened, aspark is obtained in it at the contacts. The spark is due to (A) a slow flux change in L (B) a sudden increase in the emf of the battery B(C) a rapid flux change in L (D) a rapid flux change in R

Q.33 In figure, a lamp P is in series with an iron-core inductor L. When the switch Sis closed, the brightness of the lamp rises relatively slowly to its full brightnessthan it would do without the inductor. This is due to (A) the low resistance of P (B) the induced-emf in L(C) the low resistance of L (D) the high voltage of the battery B

Q.34 Two coil A and B have coefficient of mutual inductance M = 2H. The magnetic flux passing through coilA changes by 4 Weber in 10 seconds due to the change in current in B. Then(A) change in current in B in this time interval is 0.5 A(B) the change in current in B in this time interval is 2A(C) the change in current in B in this time interval is 8A(D) a change in current of 1A in coil A will produce a change in flux passing through B by 4 Weber.

Q.35 Which of the following is true for an ideal transformer(A) Total magnetic flux linked with primary coil equals flux linked with secondary coil(B) flux per turn in primary is equal to flux per turn in secondary(C) induced emf in secondary coil equals induced emf in primary(D) power associated with primary coil at any moment equals power associated with secondary coil

Q.36 A circuit has three elements, a resistance of 11W, a coil of inductive resistance 120W and a capacitivereactance of 120W in series and connected to an A.C. source of 110 V, 60 Hz. Which of the threeelements have minimum potential difference?(A) Resistance (B) Capacitance(C) Inductor (D) All will have equal potential difference

Q.37 The reactance of a circuit is zero. It is possible that the circuit contains :(A) an inductor and a capacitor (B) an inductor but no capacitor(C) a capacitor but no inductor (D) neigher an inductor nor a capacitor.

Q.38 In a series R-L-C circuit, the frequency of the source is half of the resonance frequency. The nature ofthe circuit will be(A) capacitive (B) inductive (C) purely resistive (D) data insufficient

Q.39 An a.c. source of voltage V and of frequency 50 Hz is connected to an inductor of 2H and negligibleresistance. A current of r.m.s. value I flows in the coil. When the frequency of the voltage is changed to400 Hz keeping the magnitude of V the same, the current is now(A) 8I in phase with V (B) 4I and leading by 90° from V(C) I/4 and lagging by 90° from V (D) I/8 and lagging by 90° from V

ANSWER KEY

ONLY ONE OPTION IS CORRECT

Q.1 B Q.2 C Q.3 C Q.4 A Q.5 B Q.6 B Q.7 AQ.8 A Q.9 A Q.10 B Q.11 C Q.12 C Q.13 C Q.14 AQ.15 D Q.16 C Q.17 A Q.18 D Q.19 B Q.20 D Q.21 DQ.22 B Q.23 C Q.24 A Q.25 D Q.26 A Q.27 A Q.28 CQ.29 C Q.30 B Q.31 D Q.32 B Q.33 D Q.34 D Q.35 AQ.36 A Q.37 B Q.38 A Q.39 C Q.40 A Q.41 B Q.42 DQ.43 A Q.44 C Q.45 A Q.46 A Q.47 D Q.48 B Q.49 DQ.50 B Q.51 A Q.52 C Q.53 B Q.54 A Q.55 C Q.56 AQ.57 C Q.58 A Q.59 A Q.60 A Q.61 B Q.62 B Q.63 CQ.64 A Q.65 B Q.66 A Q.67 D Q.68 D Q.69 B Q.70 CQ.71 A Q.72 A Q.73 C Q.74 B Q.75 D Q.76 A Q.77 CQ.78 D Q.79 D Q.80 C Q.81 D Q.82 A Q.83 D Q.84 CQ.85 B Q.86 D Q.87 B Q.88 B Q.89 A Q.90 C Q.91 AQ.92 D Q.93 B Q.94 C Q.95 D Q.96 C Q.97 D Q.98 AQ.99 B Q.100 D Q.101 D Q.102 C Q.103 C Q.104 B Q.105 C

ONE OR MORE THAN ONE OPTION MAY BE CORRECT

Q.1 B Q.2 C Q.3 C Q.4 BQ.5 B Q.6 A,C,D Q.7 A Q.8 AQ.9 B Q.10 B,C Q.11 C Q.12 B,DQ.13 A,B Q.14 B Q.15 A Q.16 DQ.17 A,B,C,D Q.18 B,D Q.19 C Q.20 DQ.21 B,D Q.22 A,C Q.23 D Q.24 A,B,CQ.25 A,B,C Q.26 D Q.27 B,D Q.28 DQ.29 A Q.30 A Q.31 A Q.32 CQ.33 B Q.34 B Q.35 B,D Q.36 AQ.37 A,D Q.38 A Q.39 D