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VIBRANTACADEMY(India) Private LimitedSrrriLPt{YStcsPractice Problems /RpTarget I lT ADUANCE-2O1 3

DATE: 23/04/2013 TIME : 90 MIN. IRP DPP, NO.-6

A

Single Choice Question :1. In the circuit shown, the a.c. source voltage varies with time as : V = E sin(cot). Then, which phasor diagram correctly depicts various phasors attime t = 0? The current through the source is represented by I, and other

have usual meanings. The values are read on the vertical axis.

IR, Ir

2. A coil of indctance L and zero resistiance is connected to a source bf variablee.m.f. at t = 0. The emf of thesource is varied with time according to the graph shown on the right, What will be the average current thatflows through the coil during time T?

(B)

0 VoT2L

3VoT2L(c)

)#(D)T

A particle of charge Q and mass M moves in a circular path of radius R in a uniform magnetic field ofmagnitude B. The same particle now moves with the same speed in a circular path of same radius R in thespace between the cylindrical electrodes of a cylindrical capacitor. The radius of the inner electrode is R/2while that of the outer electrode is 3Ri2. Then the potential difference between the capacitor electrodesmust be

?

4.

c,^, QB2R21ln31(c) ff (D)None

A particle of specific charge (q/m) is projected from the origin of coordinates with initial velocity [ui - vj].Uniform electric and magnetic fields exist in the region along the +y-direction, of magnitudes E and B. Theparticle will definitely return to the origin once ifis an integer (B) (u2 +v2)1t2

BrE is an integer

vB(l 2"E13 ,. an inteserrcE uB(D) nE is an integer

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5. of charges +Q and -Q are projected from the same point with a velocity v in a region ofetic field B such that the velocity vector makes an angle 0 with the mainetic field. Theirand 2M, respectively. Then, they will meet again for thefirst time at a poiit whose distancefrom the point of projection is2rcMv cos 0ln; oe

Subjective:

7.

A long horizont in a vertical plane and is in equilibriumat a height of 0 xed in a horizontal plane and carries asteady current it executes S.H.M. and find the timeperiod.

U \c) Kcd-.t-l,! toff watlriq A= [,ni ]a.

8.

(A) For what value of or will resonance occur, i,e, the current fed by the source and its voltage will be inphase?(B) Find the average power being fed into the circuit by the source at resonance.(c) Assuming resonance, find the charge 'q' on the capacitor as a function of time.In the circuit shown on right, the switch is closed at t = 0. The capacitor had an initial charge = 2CV whosepositive side is marked (+) in the figure. Find the charge on the capacitor as a funciton'of tir" for t > O,assuming the side marked (+) as positive. Also plot its graph.

Q- =e/ [ l{- eos

In the circuit shown on the right, the switch is initially open. lt is closed at t = 0. The cell has an emf = V andthe inductor is ideal. Let the current in the inductor ai any time t > 0 be equal to I. The connecting wires have

L1$Jut9.

no resistance.(A) Form a differentialequation between variables I and t.(B) Find I = I(t) and ptot it(C) Find the current through R as

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The circuit shown is fed by an a.c. source having "'n1= (15 V) . sin (2000,where time t is in seconds. Coil-1 has a resistance = 3f) and inductance20 mH, while coil-2 has a resisance = 6C) and inductance 40 mH. Find thevoltages across the two coils, V, and Vr, as funcitons of time, t.

KoJ LLooL- g)A perfect conductor of mass M is free to slide without friction on two horizontal conducting parallel rails,which have a separation = d between them. An ideal inductor of inductance L is connected between oneside ends of the two rails. Auniform and constant magnetic field B, directed vertically upwards, exists in theregion. The conductor is given an initial velocity v0 away from the inductor side end. Find its maximum

11.

12.

displacement from the initial position. Also find the avover the time peirod of the periodic motion of the co

The figure shows a perfectly conducting ring of radiusplane. Athin conducting rod of mass'm'and resistanabout a vertical axis passing through the center of the ring, maintainingsliding contact with the ring at all times. A uniform and constant magneticfield of magnitude B exists in the region, directed vertically upwards. Att = 0, the switch S is closed. The battery has an emf = E, and zero internalresistance. Neglecting the self-inductance of the ring-sliding rod system,find the angular velocity of the rod as a fnction t > 0, and plotthisfunction tr- &E- (" t_ t-K\L \

13. Find the induced current in a square loop of side L, resistance R and negligible self-inductance if it is placedclose to a long straight wire. Both are coplanar, with two sides of frame parallel to the wire. The distance

v4.between wire and nearer parallel side of the frame isA square shaped wire loop of sirie 1m is placed in a retime variant magnetic field, with the plane of the loop pfield. The magnetic field varies with time as : B = fut, where l" = 2 T.s-l and A t--.1B't' is time. The four sides of the frame are made of different materials. Theresistance of the side AB of the wire frame is 1O, of BC is 20, of CD is 4Cl,and that of DA is 5f). Find the potential difference between the pointsA and C. -b-\

15. In the figure shown, the wire frame is in the shape of an equilateral triangleof side L. lt carries a current I. Find the magnitude of magnetic field at apoint located out of the plane of the paper, at a distance L from the centroid-- 0, and itsMbrant Academy (I) Pvt. Ltd. 'A-14(A)" Road No.1, Indraprastha I