Electromegnetic Induction & Alternating Current

5/24/2018 Electromegnetic Induction & Alternating Current

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I JEE dvancedl I ITJEE1 A,unifo rmly wound solenoidal co il of self inductance1.8 x lo4 henry andresistance.6 ohm is bro ke nu p into twoidentical coils. These identical coils are then connected inparallel across a 15-volt battery ofnegligible resistance. Theti m e constan tforthe current in the circuit is ........... econdsand the steady state current through the battery i s ..............

amperes. (1 98 9 - 2 Marks)2 In a straight conducting wire, a constant curren t is flowingfrom left to right due to a source of emf. When the source isswitched off, thedirection of the induced current in the wirewillbe..... (1993 - I Mark)3. The network shown infigure is part of aco mp lete circuit:If at acertain instant' the current (I) is 5A, and is decreasing

at ar at e of 1.03.A/s hen V - V = .....V (1997C - 1 Mark)I- iA I Q I ~ V nl11 , .

1 An e.m.f.'can be induced between th e two en ds of a straightcopper wire ivhen it is moved throug h a uniform magneticfield. (1980)2 A coil of metal wire iskept stationary in a non-uniforirmagnetic %Id. An e.m.f.is induced in the coil. ,(1986 - 3.Marks)3 A conducting rod AB moves to the x -axis (see Fig.)in auniform magnetic field pointing in the positivez-direction. The end A of the rod gets positively charged.. I 1l98 - 2 Marks)

-1 thin circular ring of area A is held perpendicular to. auniform magnetic field of inductionB.A small cutis made inthe ring and a galvanometer is connected across the endssuch that the total resistance o f the circuit is R. When thering is suddenly squeezed to zero area, the charge flowing

through the galvanometer is (1995s)

2 A thin semi-circular conducting ring of radius R is fallingwith its plane vertical in horizo ntal magnetic jnduction .At the position MNQ the speed of the ring is v, and thepoter~ tial ifference @evelopedacross the ring is

. ..

. .

M , Q(a) zero (1996 - 2 Marks)b) B V Z R ~ / ~nd is at hii he r potential(c) nRBv and Q i s at higher potential(d) 2RBv and Q is at higher potential.:

3 Two identical circular loops ofme tal wire are lying on atablewit'hput touching each other. Loop-Acarries a current which,increases with time. In response, th e loop-B(a). :remains stationaty (1999s- 2 Markb) is attracted by the loop-A(c) is repelled by th e loop-A .(d) rotates about its CM, with CM fixed

4. A coil ofinductance 8.4 m iidiesistance 6 is connectedto a 12 V battery. The current'in the coil is 1.0 A atapproximately he time , (1999.9 - 2 Marks)'(a) 500 s. . , ( b ) 2 5 s , ,c) 35 ms (d) l m s

5 A uniform but time-varying m agnetic field B(t) exists in acircular region of radius a and is directed into .the plane ofthe paper, as shown. The magnitude of theinduced electricfield at point P at a distance r from the centre oft he circularregion . , (2000s)

(a) is zero w b) decreases as I/r , .(c)- increases as r . (d) decreases as 119

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P 404 Topic-wise Solved Pap ers PHYS~ S6 A coil of wire having inductance and resistance has a 11 When an AC source of emf e = E,, sin(100t) is connectedconducting ring placed coaxially within it. The coil is across a circuit, the phase difference between the emf e andconnected to a battery at time t = 0, so th ata time-dependentcurient l,(t) starts flowing through the coil. If Z2(t) is thecdrren t induced in the ring; and B (t) isth e magnetic field at .the axis of the coil due io I,.(t); then as a function of time

t>O), the ~jroduct i(t) q t ) 2000S)(a) increases with timeb) decreases with tim e(c) does not vary with time(d) passes through a maxim um

7 A metallic square loop ABCD is moving in its o h lanewit velocity v in a un ifonn magnetic field perpendicular toit s plane as shown in the figure. n electric field is induced ,

2001s)

. 12

the current i in the circuit is observed to be 7~14 s shownin the diagram. If the circuit consists possibly only of R-Cor R-L or L-C in series, find the relationship between thetwo elements 2003s)

(a) R = l k n , C = I O p F b) R = l k n , C = l p F(c) R = l k n , L = I O H (d) R = l k R , L = l HA small bar magnet is being slowly inserted with constantvelocity.inside iso len oi d aB shown in figure. Which graph

(a) in AD, but no t in BC b). in BC, but not in AD best represents the relationship between emf induced with(c) neitheiin AD nor in BC (d) in both AD and BC time 2004s)8 TWO circular coils can be arranged in any of the three.situatio ns shown in th e figure. Their mutual inductance willbe 2001s)n

a) b) 4(a) maximum in situatio n (a) b) maximumin situation b)(c) maximum in situat ion (c) (d) the same all situatioris

9 As shown in the figure, P and Q are two coaxial conductingloops separated by some distance. When the switch S isclosed, a clockwise current p flows in P (as seen by E) andan induced current lp, lows in Q , The sw itch remains closedfor a long time. When S1s opened; a current flows in Q.Then the direction ZQ, and ZQ2 (as seen by re2002s)

(a) respectively clockwise and anti-clockwise(b) both clockwisec) both anti-clockwise(d) respectively anti-clockwise and clockw iseA short-circuited coil is placed in a time-vary ing magneticfield. Electrical power is dissipated due to the current induced.in the co il. 1f the num ber o f turns were to b.e quadrup led andthe wire radius halved, the electrical power dissipated wouldbe 2002s)(a) halved b) the same(c) doub led (d) quadrup led

13 An infinitely long cylinder is kept parallel to an uniformmagnetic field directe d along positive z-axis. Thedirection of induced current as seen from the z-axis willbe 2005s).(a) zerob) anticlockwise ofthe .+ve z axis ,

(c) clockwise of the +ve xis(d) along the magnetic field14. Find the time constant (inp or th e given RC circuits n hegiven order respectively 2006 3M, -1)




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ELECTROMAGNETICINDUCTION ALTERNATING CURRENT

15. The figure shows certain wire seg men ts joined together toform a coplanar loop. The loop is placed in a perpendicularmagnetic field in the direction going into the plane of thefigure. The magnitude of the field increases with time. I I andI2 are the currents in.the segments ab and cd Then, (2009)

X X X X X X(a) I l >I2b) I l < 1 2 . . 5(c). I , is in the direction ba and I2 is in the direction cd(d) I I is in the direction ab and 1 is in the direction dc

16. An AC voltage source'of variable angular frequency andfixed amplitude Vo s connected in series with a capacitan ce 6.C and an electric bulb of resistance R (inductance zero).When is increased (2010)(a) the bulb glows dimm er .b) the bulb gloivs brighter(c) total impedance of the cir cu it is unchang ed(d) totai impedance of thec ircu it increases

1 . L, C i d represent the physical quantities, inductance, .capacitance and resistance r&pectively. T he combination(s)which have the dimensions of frequency are 7(1984- Marks)(a) IIRC b) R/L(c) 1 / a (d) C/L

2 A conducting square loop of side L and resistan ce R movesin its plane with a uniform veloc ity v perpendicular to one ofits sides. Amagnetic induction B, constant in time and space,pointing perpendicular and into the p la ne sf the loop exists,everywhere. (1989 2 Marks)~.

The current induced in the loop is:(a) BLv/R clockwise b) BLv/R anticlockwise(c) 2BLv/R antic lockwise d) zero.Two different coils hav e self-inductances L, = 8 mH and L2= 2 mH. The current in one coil is increased at a constantrate. Th e cu rrent in the seco nd coil-is also increased at thesame constant rate. At a certain instant of time, the powergiven to the two co ils is the same. At that time, the current,the induced voltag e and the energy stored in the first coilare i l Vl and W I espectively. Corresponding values for thesecond coil at the sam e instant are i2, V2and W2 espectively.Then: . (1994 2 Marks)il 1(a). -=-i2 4A small square loop ofw ire of side is placed inside a largesquare loop ofwire of sid e L(W>[). T he loops are co-planar.and their centres coincide. The mutual inducta nceof thesystem is proportional t o (1998s 2 ~ a i k s )(a) i/L b) l2IL(c) L11 (d) L2 /iThe S I unit of inductance, the henry, c& be written as(1998s- .?Marks)(a), weberlampere b) volt-secondlampere(c) jo le/(ampere)' (d) ohm-secondA metal rod mov'es at a constant velocity in a directionperpendicular t i ts length. A constant, hiform magneticfield exists in space in a direc tion perpendicular to the roda s well as its velocity. Select the co rrect statement(s) fromthe following (l998 - Marks)(a) The entire rod is at the'same electric potential.b) There is an electric field in the rod:(c) The electiic potential is highest at the centre. f the rodand decreases towards its ends.(d) f i e electric potential is lowestat the centre of the rod,and increases towards its end s. 1A seiies R C c ircuit is connected to AC voltage source.Consider two cases; (A) when C is without a dielectricmedium and EX when C is filled with d ielectric of constant4 :The 'current I, through the resisto r and voltage V acrossthe capac itor are compared in the two cases. Which of thefollowing islare true? (2011)

(c) V > V (d) v < V;




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, .. . .P 406 Topic-wise Solved Pap ers - PHYSICS , .8 . In thegiven circuit, the AC source has = 100 rad/s. 4. A square metal wire loop of side 10 cms and resistanceConsidering the inductor and capacitor to be ideal, the correct 1 ohm is moved with a constant velocity vo in a unifom~

I

choice@) s (are) (2012) magnetic field of induction B= webers/m2as shown in the100p-F lW figure. The magnetic field lines are perpendicular to theplane of the loop (directed into the paper). The loop isconnected to a network o f resistors each of value 3 ohms.The resistances of th e lead wires OS and PQare negligible.

Wh at should be ,the speed of the loop so as to have a .steady current of 1 milliampere in the loop ? Give the, , direction of current in the loop. (1983 - Marks), _ _ _ _ _-....._.. v+ .

Q . .Ca) The current through the circuit, I is 0.3 A x x

b) Th e current through the circuit, I is 0 . 3 f i ~ . : x x : .(c) The voltage across 100 nr es ist or =.~O V , . x x x xL . . . .(d) The voltage across 50 5 resistor = 10 V .9 A current carrying infinitely long wire is'kept along the 5 Space is divided b y the line AD into two regions. Region Iis fielilfree and the Region II ha s auniformma gnetic field Bdiameter of a circular wire loop, without touching it, the. :correct statement@) s(are) directed into the plane of the paper.,ACD is a semicircularf2012) . conducting loop of radius with centre at 0 the plane of. (a) The emf-ind uced in the loop is zero if the current is the loop being in the plan e o f the paper. The loop is nowconstant. mad e to rotate with a constant angular velocity bout anb) The emf inducid in the loop is finite if the clirrent is . ,axispassinghrough and the perpendicular to the plane: . constant. of the paper. The effective resistance of th e loop is R(c) T he em f induced in the loop is zero if the current , (1985 6 Marks) :decreases at a steady rate. .~ ~ ~ i o n - 1 egiordl(d) The emf induced in the loop is infinite if the currentdecreases-at a steady rate. X X X X XX X X X X1 i 1 X x B x Xc . X X X X X1 A current from A to B is increasing in magnitude. What is X X X X Xthe d irection of induced cuke nt, if tiny, in the loop a s shown ,

X X X X X.in the figure?. , i j Obtain an expression for the magnitilde oftlie inducedcurrent in the loop.

, . (ii) Show the direction o f the curren t when the loop is. . entering into the Region 11.(iii) Plot a graph between the induced e.m.f and the time of

~ . . rotation for twope riod s of rotation.A , ; , - B . 6. Two long ~a ra ll e l orizontal rails, a distance d apart and2. .The two rails bf a railwayh ack , insulated from each other and each having a resistance h per unit length, are joined at, the ground, are connected io a milli voltmeter. w h a t is the one end by a resistance R. A perfectly con ducting rod MA

, readingofthemilli voltmeterwhen atrain travelsat aspee d of of mass m is free to slide along the rails without friction180 kmih ouralong he track, given that the vertical component (see figure). There is a uniform magnetic field of inductionof earth's magnetic field is 0.2 x 10 webe r/m2'& he rails are normal to the plane of the pa per and directed into the paper., separated by 1 meter? (1981- 4 Marks) A variable force F i s ap plie dto the rod MNsuch that, as the3. Three identical closed coils A, and Ca re placed with their rod moves, a constant current flows through R.planes parallei to one another. Coils A a n d C can y equ al (1988 6 Marks)currents as shown in Fig. Coils an d' ca re fixed in position. x . x x M , x; and coil A is moved towards B withun ifomm otion. Is thereany induced current in ? If no, give reasons. If ye s markthe direction of the induced current in the diagram.

, (1982- 2 Marks) FX

x x X N x x .(i) :Find the velocity of the rod and the applied fo rc e ,O sfunction of the distance x of the rod from R.. A B C (ii) %'hat fraction of the work don e per second by F isconverted h t g heat ?

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CTROMAGNETICINDUCTION ALTERNATING CURRENTA circuit containing a two p osition switch S is shown in fig: 10.

. . (1991 4 +4 Marks

10m(a) The switch S.is in pos ition '1'. Find the potential.difference V - VBand the rate of production of jouleheat inR ,. .@ If now the switch S s put in position 2 at t = 0 fmd(i) steady current in R4 and(ii) the timew hencurrent inR, is half the steady value.Also calculate the energy stored inthe inductor L at thattimeA rectangular frame ABCD mad e of a uniform metal wire,has a straight connection between and F made of thesame wire, as shown in Fig. AEFD is a square of side Im,and EB =PC= 0.5m. The entire circuitis placed in steadily'increasing, uniform magnetic fieid direc ted into the plane of .the paper and normal to i t The rate of change of themagnetic field is 1T ls. The resistan ce per unit length of thewire i s i n l m . . Find the magnitudes and directions of the ,curren ts in the Hegments AE, BE and EF. (1993-5 Marks 12.

A metal rod OA of mass m nd length r is kept rotatingwith a constant angular me ed in a vertical plane about ahorizontal axis at the end 0 The free end A is arranged.toslide without friction along a fixed conducting circular ringin the sam e plane as that of rotation. Auniform and constantmagnetic induction is appliedp erp~n dicularan dnto the .plane of rotation shown in the fig ure below. An inductorLa nd external resistance R are connected through aswitchSbetween the point nd a point C on the ring to fo rm anelectrical circuit. Neglect the resistance of the ring ank th erod. Initially, the switch is open. (1995 I 0 Marks

,? Y

. L(a) W ha t is the induced emf across the terminals of theswitch? .b) The switch Si s closed at time t = 0.i) Obtain an expression for the current as a hnctio noftime. ' .ii) In the steady state, obtain the time depen denceof the torque.required to intiintain the constantangular speed, given that the rod OA was alongth e po sitive X-axis at t = 0.A solenoid has an inductance of 10 henry and a resistanceof 2 ohm . It is connected to a 10 volt battery. How long willit take for the magnetic energy to reach 114 of its maximumvalue? (I996 3 Marks-+An infmitesimally small bar magnet ofdipo le mom ent M is

pointing and moving with the speed vi n the 2 direction..A small closed circular conducting loop of radius a andneglig ible self-inductance lies in the y-z plane.with its centerat x = 0, an d its axis coinciding with the x-axis. Find the forceoppo sing the motion of the mag net, if the resistance of theloop is R. Assume that the distance x of the magnet from thecenter ofth e loop is much greater than a. (I997C - 5MarksA pa ir of parallel horizontal conducting rails of negligibleresistance shorted at one end is fuced on. a table. T he distancebetween the rails is L. A conducting massless rod ofresistance Rc an slide on the rail? frictionlessly. The rod istied to am assless string which passes over a pulley fixed tothe edge of the table. Am ass m tied to the other end of thestring hangs. vertically: A co nstant magnetic fie ld B existsperpendicular to the table. If the system is released fromrest, calculate. . (1997- Marks. I , .

LOarallel vertidal metallic rails AB and CD are separated 13:by 1 m: They are co luiected at two ends by resistances R,and R s shown in Figure. A horizontal metallic bar L ofmass 0.2 kg slides withou t friction ve rtically down the railsunder the action of gravity. There is a uniform horizontal . ,magnetic field of :6Tesla perpendicular to the plane of therails. It is observed at -when the terminal velocity isattained, the powers dissipated in R , and Ri re 0.76 Watt . 'and 1.2 watt respectively. F q ~ dhe term inal velocity of thebar L and the vayues of R, and R2. (1994 6 Marks

t i . .

[i the terminal velocity achieved by the rod, and(ii) the a cceleration of the m ass at the instant when thevelocity of the rod is half the terminal velocity.




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-P.408 Topic-wise Solved Pape rs - PHYSICS14. An inductor of inductance 2.0 H s conne cted acrosscharged capapitor of capacitance 5:0 pF, and the resulting

LC circuit is set oscillafing at its natural frequency. Let Q. denote the iristantaneous charge on the capacitor, and I the

. current in the circuit. It is found that the m aximum value of Q . sis 240 pC. (1998 8 Marks) R , .. ..

, . ,(a) ~ h e n Q 100 PC. what is the v alue o f Idltdtl?.b) When Q = 200 pC, what is the value of I ? 18 A rectangular loop PQR S made fro m a uniform wire has(c) Find the maximum value of I length q width b a n d m ass m. It is free to rotate about the(d) When I s equal to one half its maximum value, what is arm PQ, which rema ins hinged alon gaho rizontal lime takenthe value o f lQl? as the-y-axis (see figure). Take the vertically ~upw ard

15 A magnetic field = 5 is into the paper in the- d i r ec t ion as the z -ax i s . A un i form magneti c f i e ldz direction. Bo'and a ar e positive con stants. A square loopFGH of side a, mass m and resistance R, in x -y plane,

starts falling under the influence o f gravity see figure) Notethe directions of x and y axes in figure. (1999 - I0 Marks)),- t x

Find j ~(a) the induced curren t in the loop and indicate its direction.b) the total Lorentz'force acting on the loop and indicateits direction, an d

(c) an expression for the speed of the loop, v(t) an d its.terminal value.16 A thermocole vessel contains 0.5 kg of distilled water at30C. A metal coil of area 5 . ' ~0 m2, number of tyrns 100,mass 0.06 kgand resistance 1.6i s lying horizontally at thebottom of the vessel. Auniform, time varying magnetic field

is set up to passvertically through the c oil at time = 0. h efield is first increased from zero io 0.8 T a t a constant ratebew een 0 and 0.2 s and then decreased to 0 and the samerate between0.2 and 0.4s. This cycle is repeaied 12000 imes.

, M a k e sketches oft he current through the coil and the powerdissipated in the coil'as functions o f time for the firsf twocycles. Clearly indicate the m agnitud esof the quantities onthe axes. Assume that no h eat' is lost to the vessel or thesurroundings. Determine the finaltem perature of the w aterunder thermal , equ i lib r ium. Spedi f i c hea t o f meta l= 50b . I k g 2 l ~ an d t h e s p ec i fi c h ea t o f w a te r , .=4 20 0 Jkg-'K-I. Neglect the inductance oft he coil.

(200 0- 10 Marks)17 An inductor of inductance L = 400 m nd resistors ofresistances R, =2i2 and R2= 2 re connected t o a batteryof emfE = 12V as shown in the figure. The interna lresis&ceof the battery is negligible. The switch S is closed at timet = 0: What is the potential drop across L as a function oftime? After the steady state is reached, the switch is opened .What is the direction and the magnitude of current throughR, as a function of time?. (2001~5 a r k s )

B = 3?+ 4i )B o exists in the region. The loop is held in thex-y plane and a current I is passed through it. The loop isnow released and is found to stay in the horizontal positionin equilibrium. (2002 Marks)-

7

X

(a). Wh at is the direction of the current I in PQ?b) Find the m agnetic force on the arm RS.(c) Find the expression for I i n terms of Bo, o band rn

19. A metal barA can slide on tw o parallel thick metallic rails.sep arate d by a dis tance A res is tance .R and an

inductance L are connected to the rails as shown in thefigure. A long straigh t wire ca rrying a constant current to s

. placed in the plane of the rails and perpendicular to them asshown. T he bar AB is hel d a t rest at a distance xo from the

. lo ng wire. At t = 0, it is ma de to slide on the rails away fromthe wire. Answer the fo llowing questions. (2002-5Marks)




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ELEcrr 0MAGNETICINDUCTION ALTERNATING CURRENT P-409di d$(a) Find a relation amon g i, - nd -, where i is thedt dt

current in the circuit and is the flux of the magneticfield due to the long wire through the circuit.(b) It is observed that at time t = T , he m etal bar AB is at adistance of from the long wire and the resistance R

carries a cuhen ti,.. Obtain an expression for the netcharge that has flown through resistance R from t = 0t o t = T. .(c) The bar is suddenly stopped at time T . The current

ithrough resistance R is found to be t time 2T Find4Lthe value of - m terms o fth e other given quantities.R

20. A square loop of side 'a' with a capacitor of capacitance Cis located between two current carrying long parallel wiresas shown. The value of I in the wires is given as I = o h o t .

2003 4 Marks)

' f a + . -(a) Calculate maxi.mum current in the square loop. :@ Draw a graph between charges on the upper plate of

the capacitor vs time.21 In a series L-R circuit (L = 35 mH and R Ia , variable,'

emfsource (V = Vosin a t) of V m =220 V and frequency 50Hz is applied. Find theourre nt amplitude in the circuit andphase o f current with respect to voltage. Draw current-timegraph on given graph (?I= 2217 . 2004 4 Marks)

22. In the figure both cells A and B are of equal emf. Find R forwhich potential difference across battery A will he zero,long time after the switch is closed. Internal resistance ofbatteries A and are r l and r, respectively ( r l , rz .

2004 4 Marks)I. .~23 A long solenoid of.radius a and number of turns per unitlength n is enclosed by cylindrical shell of radiusR. thicknessd ( d < < R ) and length L. A variable current i= io sinwt flowsthrough the coil. f the iesis tinty of thematerial of cylindrical

shell is p, find the induced current-in he shell.2005 4 Marks)

I@- IEach question contains statements given in two columns, which have to be ma tched. The statements in Column-I are labelled A,B, C and D, while the statements in Column-II are labelled p, q r, s and t .Any given statement in Column-I can have correctmatching with ONE O R MORE statem mt(s )'in Column-II. The appropriate bubbles correfpon ding to the answers to thesequestions have to b e darkened as,illustrated ih the, ollowing &ample :lft he correct matches are A-p, s and ; B-q andr ; C- p and q; a ndD -s then the correct darkening ofbubbles will look like the given.

~ . q r t

1 You are given many resistances, capacitors and inductors. These are connected to a variable DC vo ltage source (the first twocircuits) or an AC voltage source o f 50 Hz frequency (the nex t three circuits) indifferent w ays as shown in Column 11 When acurrent I (steady state for DC or rms f orA C) flows through the circuit, the corresponding voltage V,and V2 indicated in circuits)are related as shown in C olum n I. Match the two 2010)




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P-410 Topic-wise Solved Pa pe rs PHYSICSc o i u m n ~ . . . . ColumnII

(A) I f 0, V is proportional t o I

,

(D) I 0 V is proportionalto I

I@ e D O H I. PASSAGE 1In th? givencircuit the capacitor C ) may he charged throughresistance R by a battery V by closing switch S I .Also when Sl isopened and S2 is closedthe capacitor isconne cted in series withinducto r (L). V

.

1 At the start, the capacito i was uncharged. When switch SIis closed and S2 is kept open, the time aonstant of thiscircuit is K. Which of the following is correct

~ 2006 SM 2)CV(a) after time interval K charge on the capacitor is

@ after time interval 2 ~ harge on the capacitor of CV( I -*(c) the work done by the voltage source will be half of theheat dissipated when the capacitor is fully charged(d) after time interval 2 ~ ,harge on the capacitor is

CV(1 -e- ) .




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. . .E L E ~ R O M A G N E T I C I N D U C T ~ ~ NALTERNATING URRENT P-4112. When the capacitor gets charged com pletely, S, is opened 6 T h e magnitude o f the induced electric field i i ~he orbit at . ,and S2 is closed. Then, . to06 -.5M -2) any instant o f time during the time interval of the magnetic. (a) at =0, energy stored in the circuit is purely in the form' field chan ge is. -.. . of magneticenergy . . B Rb) at any.time > 0, current in the circuit is in the same ("1direction(c) at > 0, there is no exchange o f knergy between the (c) BR '(d) 2BR

inductor and capacitor 7. T h e cha ngeJn the magnetic dipole moment associated with(d) at any time t z . 0 , instantaneous current in the circuit the orbit, at the end oft he time interval ofthem agne tic fieldrT change, ism ? y b e v \ j ' - ;, , , , ; .L BQR'

3 Given that the total charge stored in the LC circuit is'^,, for (a) Y B Q R ~ . by - , .0, the charge on th e capacitor is 2006- 5M -2) ~. . .B Q R ~ .-(c) YY (d) Y B Q R ~

d 2 e(c) Q= -LC- 1 d 2 Q(d) Q =dt i l2..

PASSAGE 2Athermalpower plant produces electric power of 600 kW -at4000V,which is to be transported to a pla ce 20 km away from the powerplant forconsumers' usage. It can be transported either directlywith a cable of large current carrying capacity or by using acombination of step-up and step-down tl.ansformers at the twoends. The drawback of the direct transmission i st he large energydissipation. In the metho d using transformers, the dissipation is. . much sma ller In this method , a step-up transformer is used at theplant side so that the current is reduced to a sm aller value. At theconsumers' end, a step-down transformer is used to supply,powerto the consumersat the specified lower voltage. It is reasonablet o assum e that the' power cable is purely resistive and thetransformers are ideal with power factor unity. All the currents

and voltages mentioned are r g ~ salues. . JEEAdv. 2013)4 If the direct transmission method with a cable of resistanceR km-' is used, the power dissipation1 (in ) duringtransmission is . .(a) . 2 @ ) . .(c) . 4 ~ . ( 4 50 .5. In. he method using the transformers, assume that the ratioo ft h e number of turns in the primary to that in thesecondary-in the step-up transformer is 1 : 10. I f the p ower,to theconsumersHas to be su pplied a t 200 V, the ratio oft he number

. of tum s in the primary to that in the Second ary in the step-. .down transfo~mers. (a) 200:l . . @ ) 1 5 0 : 1

(c) 1OO:l (d) 5 0 : 1 :PASSAGE 3 ~A point charge Q is moving in a circular orbit ofr adiu sR inthe xy plane with an -ang ula ~ elocity w This can be considered asQ wequivalent to a loop can yin g a steady current A uniform.a*magnetic field along the positive z-axis is now switched on, whichincreases at a conkant rate fro m 0 to in onesec ond. Assumethat ihe radius of the qrbit remains constant. The application ofthe m agnetic field induces an emf in the orbit. The induced emf isdefined as the work don eby an induced electric field in moving aunit positive charge around a closed loop. It is known that, for anorbiting charge, the magnetic dipole moment is proportional tothe angular momentum with a proportionality constant y.JEE Adv. 2013)

1. Statement-1 : vertical iron rod has coil ofw ire wound overit at the bottom end. An alternating current flows in the coil.The rod goes through a conducting'ring as shown in tliefigure. The ring ca n float at a certain height ab ove the co.il.2007)

. . .S t a t em en t 3 : n the above situation, a current is induced.in'the ring which interacts wit hth e horizontal component ofthe magnetic field to produce an average force in tlie upwarddirection. . .(a) Statem ent-l i' i ~ r u e , tatement-2 is True; Statement-;is a co rrect explana tion for Statement-1(b) Statem ent-1 is True, S tatem ent-2 is True ; Statement-:is NOT a correct explanation for statement-1 ..(c) Statement-1 isT rue , Statement-2 is False . .(d) Statement-l is False, Statement-2 isTr ue.

-1 A series R C combination is connected to an AC voltage ofangular frequency o = 500 radianls. If the impedance oft he

R C circuit iS ~ ith e time constant in millisecond) ofthe circuit is2. A circular. wire loop of radius R isplaced in the x-y plane centered at theor igin 0 square loop of s idea(a


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P-412 Topic-wise Solved Pap ers PHY SICSi i J Main lEEE

1 The power,factor of a nA C circuit having resistance (R) and 10: In anZ CR se ries a.c. circuit, the voltage across each of theinductanc,e (L) conn ected in series.and an angular velocity, components, L , C and R is 50V. The voltage across the LCw is 'combinationwill be [ZOO41(a) RfwL b) hY(R2+ w2L2)'(c) O L I R (d) RI(R' - oZ ~ 2 ) i n2. A conducting square loop of side L and resistance R movesin its plane with a uniform velocity v perpend icular to one o fits sides. Amagnetic induction B co nstant in time an d space,pointing perpendicular and into the plane at the loop existseverywhere with halfth e loop outside the field, as shown infigure. The induced em f is [2002]jFt . , ,:(a) zero b). RvB(c) VBLIR (d) vBL

3 The inductance between and D is [2002]I(a) 3.66H b) 9 H (c) 0.66H (d) 1 H.In a transformer, number of turn s in the primary coil are 140and that in the s econd ary coil are 280. If c urrent in primarycoil is 4 A, then that in the secon dary coil is [2002](a) 4 A ( b ) 2 A ( 4 6 A (d) 1 0 ~ .Two coils are placed close to each other. The mitualinductance of the pair of coils depend s upon [ZOO31(a) the rates at which currents are changing in the twocoilsb) relative oosition and orientation of the two coils(cj the materials of the wires of the coils(d) the currents in the two coils

6 When the current changes from +2 A to -2A in 0.05 second,an e m f . of 8 V is induced in a coil. The coefficient of $elf-induction of the co il is [ZOO31(a) 0.2H b) 0.4H (c) 0.8H (d)O.l H7. In an oscillating LC circu it the maximum charge on the .capacitor is Q. The cha rge on the cap acitor when the energyis stored equally between the electric an d magnetic field is

, 120031 .

8 The core of any transformer is laminated so as to [ZOO31(a) 'redu ce the energy loss due to eddy currentsb) make it light weight(c) make it robust and strong(d) increase the Secondary voltage9 Alternating current can not be m easured by D.C. amm eterbecause (2~041(a). Average value of current for complete cycle is zerob) A.C. Changes direction .

(c) A.C. can not pass through D.C. Ammeter ,(d) D.C. Ammeter will get damaged.

(a) loOV b) 50& V(c) 5 0 ~ (d) 0 V(zer0)

11 A coil having n turns and r esistance RC2 is connected witha galvanometer of resistance 4RC2. This combination ismov ed in time t second s from am agn etic field Wl weber toW2 weber. The induced cu rrent in the circuit is [ZOO41(W2 -w,(a) - Rnt(W2 -4 n ( w 2 - 6 )(c) - 5 Rnt ( 4 - Rt

12. In a uniformma gnetic field of induction B a wire in the form. of a semicircle of radius r rotates a bout the diameter of thecircle with an angular frequency co The axis of rotation isperpendicular to the field. If the total resistance of the circuitis R he mean power generated per period of rotation is2(Bnr w)

@) 8R

In a LCR circu it capacitance is changed from C to 2 C. Forthe resonant frequency to remain unchanged, theinductance should be chang ed from L to [ZOO41(a) Z b) 2 L ( 4 4 L (dl U 4A metal conductor of length 1m rotates vertically about oneof its ends at angular velocity 5 radians per second. If thehorizontal component of earth's magnetic field is 0 . 2 ~04T,then the e.m.f. d evelope d betwe en the two ends of theconductor is [ZOO41(a) 5mV b) 50pV (c) 5 i V (d) 50mV15. One conducting ube can slide inside another as sh 0. min figure, maintaining electrical contacts between the tubes . .The magnetic field B is peipendicular to the plane of thefigure f each tube movestowa rds the other at a constantspeed v, then the emf induced in the circ uit in terms of B, 1'and v where I is the width of eac h tube, will be [ZOO51

(a) - Blv b) Blv(c) 2 Blv (d) zero16. The self inductance oft he motor of an electric fan is 10 H. Inorder to impart maximum power at 50 Hz, it should beconnected to a ca pacitance of [ZOOS](a) ~ P F b) 41rF (c) ~ P F ( 4 1 PF




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E L E a O M A G N E T I CINDU TION ALTERNATING CURRENT17. The phase difference between the alternating current and 26.

emf is E Which of the following cannot be the con stituent2' . of the cucuit? [2005] .(a). R, . (b) alone (c)' L alone (d) L, C 27.18. A circuit has a resistance of 12 ohm and an impedance of 15

ohm. The, power factor of the circu it will be 120051(a) 0.4 b) 0.8 , (c) 0.125 (d) 12519. A coil of inductarice 300 mH and resistance 2 11 isconnectedto a source of voltage 2 V. The iur ren t reaches half of itssteady state value in [2005](a) 0.1 s b) 0.05 s (c) , 0.3 s (d) 0.15s .& 28.20. Which ofthe following units deno tes thedimension ~where Q denotes the electric charge? [2006](a) Wb/m2(c) Wm2 b) Henry(H)(d) Weber (Wb)21. In a series resonant LCRcircuit, the voltage across R is 100

volts and R = 1 kQ with C =2pF. The reson ant frequency wis 200 radls. At resonance the voltage across L is (20061(a) 2.5 x lo-= V .(b) 40V

An ideal coil o f 1 0H is connected in serieswith a resistanceof 5 n and a battery of 5V. 2second after the coiniection ismade, the current flo wing in ampere in the circuit is [2007](a) (1-e-.') b) ( 1 - 4 c) e (d) i ITwo coaxial solenoids are made by winding thin insulatedwire over a pipe of cross-sectional area A = 10 cm2 andlength = 20 cm..If one o fth e solenoid has 300 turns and theother 40 0 turns; their mutual inductance is [2008]-(p o= 4n x 10-7TmA-')(a) 2.4n x 10 H (b) 4.8n 104H(c) 4. 8n x1 04 H (d) 2.4n 104H .

~ ~(c) 250V (dj 4 x lo-3 v An inductor of inductance L = 400 mH and resistors of22. ,In an AC generator, a co il with Ntu rns, all of the same area feiistance R ~ ' 211 and R2 = 2Q are connected to a batteryA and total resistance R, rotates with flequency w in amagnetic field B. Th e maximum va lue of em f generated in of emf 12 V as shown in the figure. he internal resistance ofthe coil is [2006] the batteryis negligible. The switchS is closed at t=O . The(a) N.A.B.ICw , b) N.A.B Potential drop acro ss L as a function oftim e is : 120091(c) N.A.B.R (d) N.A.B.w23. The flux linked w itha coil at any instant 't' is given by 12 -3rv .(a), y e b) 6(1- e (0 .2 )~ ~$ = lo t2 -5 0 t+ 2 5 0 (c) 12e&lV (d) 6e-51VThe induced emf at t = 3s is 120061 29.' A rectang ular loop has a sliding connector PQ of length I' , (a) -190V b) -1OV (c) 1OV (d) 190V and res istance R 11 and it is 'moving with a speed v as24. An inductor (L = 100 mH), .a resistor (R = 100 11) and a shnwn .The,set-up i s placed in a uniform magnetic fieldbattery (E= 100V) are initially connected in series as shownin the figure. After a long tim e the b attery is disconnected going into the plan e of the paper. The three currents 11,I2and I areafter short circuiting the points Aa nd B. Th e cun ent in the 12Olol .circuit ms after the short circu it is [2006]

R Q. . B.-.-.-.I ..-...

E Q(a) l/eA b) .eA ( c ) O . l A ( d ) l A25:' In an a.c. circuit the voltage applied is E = Eo sin a t. The Blv 2Blv(a) 11=-12=- I=-6R 6Rresulting current in the circuit is I = IOin Blv 2Blv , ~power consum ption in the circuit is given by [2007] b) 1 1 = 1 2 = - , I = -3R 3R

a ) P = ~ E , I ~ EoIo(b) P = - Z lr(c) i = I~= I = .E I ,(d) P =(c) P=zero ~

2 Blv . Blv(d) Il,= I2= -, I =R 3R




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1 1P 41430. In the circuit shown below, the key K is closed at t = 0. Thecurrent through the battery is [2OlO]

rnK

V R ~ R ~ , ' ~ v. . ( a ) a t t = O a n d - a t t = GJ32

V V(RI +R2)b) s, t t . = O a n d i t t = m . .Rl R2

31. In a series LCR circuit R = 200Q and the voltage and thefreq uen cy ofthem?? supply is 22 0y. md 50 Hzrespectively.On taking out the.capacitance froni the circuit the currentlags behind the voltage by30 . On taking out the inductorfrom the circuit the current leads the.vo ltage by 30. Th evow er dissipated in the LCR circuit is lZOlOl(a) 305f b) 2 1 0 W(c) Zero W (d) 242 W . .32. A boat is .mov ing due, east in a region wh ere the earth'smagneticfield is 5.0 IO NA-' m-I duen orth and horizontal.The boat carries a vertical aerial 2 m long. Ifth e speed of theboat is 1.50 ms-I; the magnitude of the induced emf in thewire ofae rial is: . . [2011](a) . 0.75mV b) 0.SOmV(c) 0.15mV (d) Im V33 . A fully charged capacitor C with initial charge q isconnected to a coil of self inductance L at t = 0. The time atwhich the energy is stored eq ually between the e lectric andthe magnetic fields is: [ZOll](a) b) x a(c) m . ~ . (4m .34. A resistor R arid pF capacitor in 'series is connectedthrough a switch to 200 V direct supply.Across the capacitoris ane on bulb that lights up at 1 20 V. Calculate the value ofR to make thebu lb light uu 5 s alter the switch has beenclosed. (log,,2.5 = 0.45 120111(a) 1 . 7 x i o ~ nIcl 3.3 10'0, b) 2.7 lo6d 1 .3x104Q\-, - - - - - - -35. ~bmbina t ion f two identiial caoacitori. resistor R and a

, dc voltage source of voltage 6 V is used ih a n experiment ona (C-R) circuit . I t is found that for a p d e l ombinatiqn ofthe capacitor the time in which the voltage of the fully. charged combination reduces to half its original voltage is10 second. For series combination the time for needed forreducing the voltagzo fthe fully charged series combinationby half is . , . [ZOllRS]

(a) 10 secand 6 5 second(c) 2.5 second (d ) 20 second

Topic wise Solved Papers - PHYSICS36. A horizontal strajght wire 20,m ong extending 6o m east towest falling with a speed o f 5.0 m/s, at right angles to thehorizo ntal com pone nt of the earth's magnetic field0.30 10 ~ b / m ~ .he instantaneous value of the e m f .induced in the wire will be . [ZOllRS](a) 3mV b) 4.5mV . .( c ) l.5mV (d) 6.O'mV37. A coil is suspended in a uniform magnetic field, with theplane o fthe coil parallel tot he magnetic lines offorce; When. a current is passed throu gh the coil itsta rts oscillating; It isvery difficult to stop. But if an aluminium plate is placedne af to the coil, it stops. This is due to : [2012]

(a) developem ent of air current when the plate is placedb) induc tion of electrical charge on the plate(c) shield ing of magn etic lines of force as aluminidm is a .paramagnetic m ate~ia l.(d) . elechomagnetic ind uctionin the aluminium plate givingrise to electroma gnetic damping..38: . A metallic rod o f length e is tied to a string of length2e aridmad e to rotate with angular speed.w,on a horizontal table. w it h one end ofthe stringfixed.Ifthere isavertical magneticfield B in the region, th e e.m.f. indu ced across the ends ofthe rod is [JEE M ain 20131

39. A cir cu lg loop of radius 0.3 cm lies parallel toathuch bigger.: circular loop ofrad ius 20 cm. The centre ofthe sman loop ison the axis of the bigger loop. The distance between their .centres is 15.cm. If acurrent of 2.0 A flows through.thesmaller loop, then the flux linked w ith bigger loop is. . 1 [JEEMainZO13](a) 9.1 x lo- weber Cb 6 lo- weber(c) 3.3 10-l1 weber (d) 6.6 x lo-? weber40. In an LCR circuit as shown below both switchesare openinitially. Now switch S1 is closed, S2 kept opm . (q is chargeon the capacitor and .r = RC is Capacitive time constant).Which of the following statement isco rrect ?[JEE Main 20131v. . . . .

(a) Work done by the battery s half of the energydissipated in the resistor(b) At t = T, q = CVI2 . ,16) A ~ ~ = ~ T , ~ = c v ( I - ~ - '( d ) A t t = 2 . t , q = C V ( l - e - )



Electromegnetic Induction & Alternating Current

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