SrrriL Pt{YStcs
VIBRANTACADEMY (India) Private Limited DATE: 23/04/2013 Single Choice Question
1.
TIME :
90
Practice Problems /Rp
Target I lT ADUANCE-2O1 3
MIN.
IRP DPP, NO.-6
:
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 at time t = 0? The current through the source is represented by I, and other
have usual meanings. The values are read on the vertical axis.
A (B)
IR,
2.
Ir
A coil of indctance L and zero resistiance is connected to a source bf variablee.m.f. at t = 0. The emf of the source is varied with time according to the graph shown on the right, What will be the average current that
flows through the coil during time T?
0
€)#
VoT 2L
(c)
?
c
(D)T
3VoT 2L
A particle of charge Q and mass M moves in a circular path of radius R in a uniform magnetic field of magnitude B. The same particle now moves with the same speed in a circular path of same radius R in the space between the cylindrical electrodes of a cylindrical capacitor. The radius of the inner electrode is R/2 while that of the outer electrode is 3Ri2. Then the potential difference between the capacitor electrodes must be
,^, (c) 4.
QB2R21ln31
(D)None
ff
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. The particle will definitely return to the origin once if
(l
vB
2"E
13 rcE
is an integer
,. an inteser
Mbrant Academy (I) Plrt Ltd. "A-14(A)"
(B)
(D)
(u2 +v2)1t2
uB nE
B
rE
is an integer
is an integer
Road N0.1, Indraprastha IndustrialArea, Kota (Raj.) Ph. 0744-2423406
tll
)
of charges +Q and -Q are projected from the same point with a velocity v in a region of etic field B such that the velocity vector makes an angle 0 with the mainetic field. Their
5.
and 2M, respectively. Then, they will meet again for thefirst time at a poiit whose distance from the point of projection is 2rcMv cos 0
ln;
oe
Subjective:
horizont 0 steady current
A long at a height of
in a vertical plane and is in equilibrium
xed in a horizontal plane and carries a it executes S.H.M. and find the time
period. 7.
U \c) Kcd-.t-l ,! toff watlr
iq
A=
[,ni
]a.
(A) For what value of or will resonance occur, i,e, the current fed by the source and its voltage will be
phase?
in
(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. 8.
In the circuit shown on right, the switch is closed at t = 0. The capacitor had an initial charge = 2CV whose positive 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/
9.
[
l{- eos
L1
$Jut
In the circuit shown on the right, the switch is initially open. lt is closed at t 0. The cell has an emf = V and = the inductor is ideal. Let the current in the inductor ai any time t > 0 be equal to I. The connecting wires have 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
BIT= "J LR Vibrant Academy (I) pvt. Ltd. ,,A-14(A)"
Road
" T- tuvti\t a4
fi) KoJ LLooL- g) t^c.rsf&oot-
10.
The circuit shown is fed by an a.c. source having
(15 V) . sin (2000,
"'n1= where time t is in seconds. Coil-1 has a resistance = 3f) and inductance 20 mH, while coil-2 has a resisance = 6C) and inductance 40 mH. Find the
voltages across the two coils, V, and Vr, as funcitons of time, t.
11.
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 one side ends of the two rails. Auniform and constant magnetic field B, directed vertically upwards, exists in the region. The conductor is given an initial velocity v0 away from the inductor side end. Find its maximum displacement from the initial position. Also find the av over the time peirod of the periodic motion of the co
12.
The figure shows a perfectly conducting ring of radius
plane. Athin conducting rod of mass'm'and resistan about a vertical axis passing through the center of the ring, maintaining sliding contact with the ring at all times. A uniform and constant magnetic field of magnitude B exists in the region, directed vertically upwards. At t = 0, the switch S is closed. The battery has an emf = E, and zero internal resistance. Neglecting the self-inductance of the ring-sliding rod system, find the angular velocity of the rod as a t > 0, and plot
fnction
thisfunction
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 placed
close to a long straight wire. Both are coplanar, with two sides of frame parallel to the wire. The distance between wire and nearer parallel side of the frame is
14.
A square shaped wire loop of sirie 1m is placed in a re time variant magnetic field, with the plane of the loop p field. The magnetic field varies with time as : B = fut, where l" = 2 T.s-l 't' is time. The four sides of the frame are made of different materials. The resistance 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 points
and
A and C.
15.
16.
v A
t--.1B
-b-\
In the figure shown, the wire frame is in the shape of an equilateral triangle of side L. lt carries a current I. Find the magnitude of magnetic field at a point located out of the plane of the paper, at a distance L from the centroid
L
--<-:a a-rr
-l-at (3
A charged partcle of specific charge q/m, is fired with velocity vo, in a region of uniform magnetic field of magnitude B, with the angle between the initial velocity and magnetic field = 60o. time will the particle be at a distance of L = 3nmvo/(qB) from its firing point?
Aft
17.
A particle of charge +1 pC and mass 1 milligram is released from rest at t = 0, in a region of unidirectional
and uniform, but time variant electric field : E = (10 V.m-l.s-1/2)i[. After 100 seconds, the electric field is switched off, and a uniform magnetic field of magnitude (1i3) x 104 T is switched on. The direciton of B makes an angle of 45o with the direction of the previously mentioned electric field. Find the pitch of the helical path taken by the particle after the magnetic field is switched on.
{ \r{ ri- fi
18.
In agravityfree region, uniform electricand magneticfieldsexistgiven by:E = Ejand B = Bk,Att= 0, a small particle of specific charge (q/m) is released from rest at the oriqin of coordinates. Find the v-coordinate of the particle as function of time 't' for t > 0, and its
Mbrant Academy (I) Pvt. Ltd. 'A-14(A)"
Road No.1, Indraprastha
I
