PH YSI CS

TARGET : JEE (ADVANCED) 2018

 


INF ORMATI O
E E ST
DPP
DAILY PRACTICE PROBLEMS

Course : VIJETA & VIJAY (ADP & ADR) Date : 20.04.2018

NO. 4

TEST INFOR MA TION

DATE : 24.04.2018 PART TEST (PT)–2
Syllabus : Current electricity,Capacitor, Magnetic field and force, Electromagnetic induction, Alternating
Current.

DPP Syllabus : Magnetic field and force, Electromagnetic induction , Alternating Current
DPP No. # 4
Total Total Marks : 159 Max. Time : 127 min.
Single choice Objective (-1 negative marking) Q. 1 to 15 (3 marks 2½ min.) [45, 37½]
Multiple choice objective (-1 negative marking) Q.16 to 24 (4 marks, 3 min.) [36, 27]
Single Digit Subjective Questions (no negative marking) Q.25 to Q.35 (4 marks, 3 min.) [44, 33]
Double Digits Subjective Questions (no negative marking) Q. 36 (4 marks, 3 min.) [04, 03]
Comprehension (-1 negative marking) Q.37 to 43 (3 marks 2½ min.) [21, 17½]
Match Listing (-1 negative marking) Q.44 (3 marks, 3 min.) [03, 03]
Questions based on column matching (-1 negative marking) Q.45 to Q.46 (3 marks, 3 min.) [06, 06]

1. In the given circuit Key is closed at t = 0. At what time the P.D across inductor is one fourth of emf of the
cell.

L L 2L
(A) n 2 (B) n 4 (C) 0 (D)
R R R

2. An electric bulb is designed to consume 55 W when operated at 110 volts It is connected to a 220 V, 50 Hz
line through a choke coil in series. The inductance of the coil in series for which the bulb gets correct
22
voltage is – (Take  = )
7
2 3 3 3 7 3 11 3
(A) H (B) H (C) H (D) H
10 10 10 10

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3. A charge particle of mass ‘m’ & charge –q is released from rest from a given position Q inside a fixed
vertical semicircular trough. For the presence and the absence of magnetic field normal reaction acting on
the charge at P are N1 & N2 respectively. Neglecting friction & assuming gravity presence. The value of
N 1 – N2 is :

Bq 2gR Bq 2gR
(A) 2Bq 2gR (B) (C) Bq 2gR (D)
2 4

 q
4. There exist a uniform magnetic field B  10Tkˆ in space. A point charge (specific charge  1 C / kg is
m
projected from (–5 m, 0, 0) with velocity 3v ˆi  vjˆ . The value of 'v' for which the charge particle will pass
through origin.
(A) 5m/s (B) 10m/s (C) 15m/s (D) 25m/s

5. Nuclear magnetic resonance with protons (H nuclei) is basis of Magnetic Resonance Imaging (MR).
Nuclear magnetic resonance uses flipping of nuclear spin determine structure of chemical compounds.
Suppose proton acts like magnetic dipole whose component along the applied field is 1.41 × 10–26J/T. The
applied magnetic field is 1.5T. What should be the frequency of radiations to be used in MRI device to flip
the spin.
(A)14 MHz (B) 10 MHz (C) 36 MHz (D) 63.8 MHz

1
6. Consider two infinite large parallel current carrying sheet. Current per unit width in both sheets is A/m.

If direction of current in both sheets is same than force per unit area on each sheet will be : (Neglect edge
effect)
–7 2 –7 2 –7 2 –5 2
(A) 10 N/m (B) 0.5 × 10 N/m (C) 2 × 10 N/m (D) 10 N/m

7. Consider two uniformly charged concentric and coaxial rings of radii R and 2R. Total charge on inner ring is
Q1 and that on outer ring is Q2. Both rings are revolving in same sense with same angular velocity about its
Q
axis. If net magnetic induction at a distance R from the centre of the rings, on axis of rings is zero then 1
Q2
is :
2 2 8 2 4 2
(A) – 1 (B)  (C)  (D) 
5 5 5 5 3 3

 
8. The space has electromagnetic field which is given as B  –B0kˆ and E  –E0kˆ . A charged particle having
mass m and positive charge q is given velocity v0 î at origin at t = 0 sec. The z- coordinate of the particle
when it passes through the z- axis for the first time is (neglect gravity through motion) :
22mE0 42mE0 2mE0 42mE0
(A) (B) (C) (D)
qB02 qB20 qB02 qB02

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9. In the ac circuit shown, XL=7 ,R=4  and XC=4 .The reading of the ideal voltmeter V2 is 8 2 . The
reading of the ideal ammeter:

(A) 3A (B) 2A (C) 4A (D) 5A

10. For the given A. C. Circuit, the energy stored in the capacitor has amplitude of :
R

XC = R

~
v = v0sint
v 02 v 02 v 02 v 02
(A) (B) (C) (D)
4R 8R R 2R

11. A source of alternating emf E = E0 sint is connected in series with a capacitor and inductor in a circuit with
1
negligible resistance. Natural frequency of LC oscillation is 0 = . If charge on capacitor at any
LC
moment is given by :
Q = Q0sint
then magnitude of Q0 is :
E0 E E0
(A) (B) 02 (C) (D) None of these
| 2  20 | L L | 2  02 |

12. A conducting wire fixed at both end is vibrating in it's fundamental mode in the plane of paper. A constant
magnetic field (B) is switched on as shown. Find the emf induced in wire at an instant it is passing through
mean position. Here a is maximum amplitude,  is angular frequency of wave of which standing wave is
formed and length of wire is .

Ba Ba 2Ba

(A) (B) Ba (C) (D)
 2 

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13. Consider a square frame of side 1m and total resistance 16 (uniformly distributed) in two regions of
uniform magnetic field. In region left to line AC magnetic field is 200 T inward and perpendicular to the
plane. In region right to the line AC magnetic field is 200 T outward and perpendicular to the plane. A
conducting rod of negligible resistance slides with uniform velocity 0.5 m/s as shown in the figure. The rod
always remain parallel to side BC. Current through the conducting rod when it is 25 cm away from side BC
is
×
D × C
× ×
×
×
A B
20 40
(A) zero (B) A (C) A (D) 10A
3 3

14. Three identical large plates are fixed at separation of d from each other as shown. The area of each plate
is A. Plate 1 is given charge +Q while plates 2 and 3 are neutral and are connected to each other through
coil of inductances L and switch S. If resistance of all connected wires is neglected the maximum current
flow through coil after closing switch is (C = 0 A/d) (neglect fringe effect)

Q1 d 2 d 3

L
Q0 Q0 2Q0 Q0
(A) (B) (C)  (D)
LC 2LC LC 2 LC

15. A metallic ring of mass 2 kg and radius 1m with a uniform metallic spoke of same mass 2kg and length 1 m
is rotated about its axis with angular velocity 1 rev/sec. in a perpendicular uniform magnetic field B of
magnitude 10T as shown if figure. If the central end of the spoke is connected to the rim of the wheel
through a resistor R of magnetiude as shown. The resistor does not rotate, its one end is always at the
center of the ring and other end is always in contact with the ring. A force F as shown is needed to maintain
constant angular velocity of the spoke then, F is equal to (The ring and the spoke has zero resistance)

(A) 10 N (B) 20 N (C) 50 N (D) 30 N

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16. Two uniform concentric coil of radii r1 and r2 (r 1 << r2) carry currents i1 and i2 respectively. If the smaller coil
is rotated slightly about one of its diameter it starts oscillating. Then choose the correct statements.
(A) The oscillations are simple harmonic in nature
(B) The frequency of oscillation is directly proportional to product i1i2.
(C) The frequency of oscillation is directly proportional to square root of r2.
(D) The frequency of oscillation is independent of radius r1.

17. The current in coil (as shown in figure) is  (centers of all the circular loops lie at same point) and angular
spread of coil is 90º, n is number of turns per unit radian and R is radius of each turn. (Assume that turns
are very close)

 0 n 2 0n
(A) B at common centre will be (B) B at common centre will be
2R R
n2R2
(C) Magnetic moment of loop will be (D) Magnetic moment of loop will be 2nR 2
2

18. A ring of mass m and radius R is set into pure rolling on horizontal rough surface, in a uniform magnetic field
of strength B-as shown in the figure. A point charge of negligible mass is attached to rolling ring. Friction is
sufficient so that it does not slip at any point of its motion. (is measured in clockwise from positive y-axis )
y
×××××××××××××××
×××××m × × × ×q × × × × × ×
× × × × × × ×× × × × × × × ×
× × × × × × × × × × v×=×/R
×××
××××× R × × × × × × × × x× ×
× × × × × × × × × × v× × × × ×
×××××××××××××××
×××××××××××××××
(A) Ring will continue to move with constant velocity.
(B) The value of friction acting on ring is Bqv cos .
(C) The value of friction acting on ring is Bqv sin .
 mg 
(D) Ring will lose contact with ground if v is greater than  
 2qB 
19. Wire frames having a shape of equilateral triangles are made as shown (resistivities are shown in figure).
All the wire frames have uniform and same cross section then magnetic field intensity at geometrical centre
is zero in:

(A) ‘’ (B) ‘  (C)    (D) V

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20. Consider a series LCR circuit connected to an AC supply of 220 V. If voltage drop across resistance R is
VR, voltage drop across capacitor is Vc = 2VR and that across inductor coil is VL = 3VR then choose correct
alternative(s)
(A) VR  220 2 V
1
(B) Power factor of circuit is
2
(C) VR = 156 V

(D) Phase difference between current and source voltage is
4

21. An AC source rated 100 V (rms) supplies a current of 10 A (rms) to a circuit. The average power delivered
by the source
(A) must be 1000 W (B) may be 1000 W
(C) may be greater than 1000 W (D) may be less than 1000 W

22. Two parallel resistance less rails are connected by an inductor of inductance L at one end as shown in the
figure. A magnetic field B exists in the space which is perpendicular to the plane of the rails. Now a
conductor of length , mass m and neglible resistance is placed transverse on the rails and given an
impulse J towards the rightward direction. Then choose the correct option (s).

B
L J


(A) Velocity of the conductor is half of the initial velocity after a displacement of the conductor
3J2L
d
4B2 2m
(B) Current flowing through the inductor at the instant when velocity of the conductor is half of the initial
3J2
velocity is i =
4Lm
3J2L
(C) Velocity of the conductor is half of the initial velocity after a displacement of the conductor d 
B 2  2m
(D) Current flowing through the inductor at the instant when velocity of the conductor is half of the initial
3J2
velocity is i =
Lm

23. Figure shows LC circuit with two inductor and two capacitors The L1
 c1
current in circuit is. given by I = 12 sin (2t + )
3
L 1 = 3H, L 2 = 2H, C 1 = 0.2 F I
select correct statement(s)
200
(A) C2 = mF c2 L2
3
(B) C2 cannot be determined from given information

(C) At t = energy in inductor (L1) is maximum.
12

(D) At t = energy in capacitor C1 must be zero.
12

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24. A nonconducting ring of uniform mass m, radius b and uniform linear B0
charge density ‘’ is suspended as shown in figure in a gravity free
space. There is uniform coaxial magnetic field B0, pointing up in a
circular region of radius ‘a’ (<b). Now if this field is switched off, then :- a b

(A) There will be induced electric field on periphery of ring, in anticlockwise sense when seen from above
(B) Induced electric field imparts angular momentum of magnitude  a2b Bo
(C) Final angular velocity of ring will be more if time taken to switch of the field (Bo) is small
(D) Final angular velocity will always be independent of time taken to switch off the field (Bo).

25. Figure shows a movable, rigid and conducting connector MN between a fixed L-shaped conducting wire.
The whole system is in horizontal plane having vertical magnetic field B and point M is pulled horizontally
with constant speed v starting from t = 0 by some external agent. Initially, at t = 0, if  = 90°, induced

current in the loop OMN is found to be zero at time t = . Find K (Given that M and N are always in
KV
contact with the L–shaped wire).
N 
B



 V
O
M
26. In a moving coil galvanometer, a coil of area  cm 2 and 10 windings is
used. Magnetic field strength applied on the coil is 1 tesla and torsional
stiffness of the torsional spring is 6 × 10–5 N.m/rad. A needle is welded
with the coil. Due to limited space, the coil (or needle) can rotate only by
90º, For marking, the 90º space is equally divided into 10 parts as
shown. Find the least count of this galvanometer in mA.

27. In the AC circuit shown, phase difference between voltage and current is  radian. What is the minimum
(2n  1)
possible positive integer value(s) of n for which   is an integer.

10 3 2 3

28. In the circuit diagram shown, XC = 100 , XL= 200  & R = 100 . The effective current through the source
is X Ampere then find out value of X :

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29. One cycle of an alternating current is shown in the graph. R. M. S. value of current from t = 0 to t = T is
2
i0 . Find x.
x
i
i0

T/2 T t

30. Consider 3 identical conducting loops kept parallel to each other such that their axis coincides. Loop (1),
loop (2) and loop (3) self inductance of each loop is L. Current in loop (1) is I1, in loop (2) I2 and in loop (3)
dI1 dI2 dI3
I3, rate of change in current in them at certain instant is , , respectively . Their mutual
dt dt dt
inductance is Mij (i.e. for 1 & 2 its M12) current in loop (1) and (3) is in same sense and in (2) its in opposite
sense :
d  d

1 2 3

 
(1) (2) (3)
dI1 dI dI L
Given that if  2 2  3 , emf induced in loop (2) is zero. Find
dt dt dt M12

31. In circuit, initially capacitor and inductor do not have any energy, Then find current through the battery in
Ampere just after switch is closed

32. In the LR circuit the switch S was closed for a long time. The ideal cell in the circuit has emf E volts.Later
on the switch is opened. The current in the resistor of resistance R ohms just after the switch was opened
XE
is , then x is
4R

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 3 4 
33. A conducting rod of length 1 m aligned along the unit vector  ˆj  kˆ  , is moving with a velocity
5 5 
 
ˆ ˆ ˆ tesla. Find the magnitude of
v  (2i) m/s. The motion take place in a uniform magnetic field B  ( j  2k)
induced emf in across the rod in volt.

34. A conductor carrying current 60A is in the form of a semicircle AB of Y

radius R and lying in xy-plane with its centre 'O' at origin as shown in

the figure. The magnitude of B.d for the circle x2 + z 2 = 3R2 in
 B

xz-plane due to current in curve AB is 10n 0. Find the value of n (n is
an integer) 
O X

Z A

35. Insulating cylinder of radius r carries a charge of surface density  on its cylindrical surface and rotates with
angular velocity  about axis of cylinder. A radial conducting wire connects the axis of the cylinder with the
cylindrical surface (it rotates together with the cylinder). The electromotive (voltage)  between the ends of
 x r y
the wire is   0 .Find the value of x + y.
2

36. A loop PQR formed by three identical uniform conducting rods each of length a = 20 cm is suspended from
one of its vertices (P) so that it can rotate about horizontal fixed smooth axis CD. Initially plane of loop is in
vertical plane. A constant current i = 10 A is flowing in the loop. Total mass of the loop is m = 60 gm . At
t = 0, a uniform magnetic field of strength B directed vertically upwards is switched on. If the minimum value
of B (in mT) is n, so that the plane of the loop becomes horizontal (even for an instant) during its
subsequent motion. Then value of n/10 is

Comprehension–1
Consider a long conducting rail, separation between tracks is , fixed in uniform magnetic field B directed
normal to the plane of rail tracks and shunted by an uncharged capacitor of capacitance C. A conducting
rod of mass m, given a velocity V0 and then kept gently and symmetrically on track as shown. Neglect any
resistance (i.e. of track and conducting rod) and any friction between rod and track. (Use B22C = 2m)

× × × B

×g ×C V0 × × 

× × ×

Answer the following 2 questions based on the given arrangement.

37. Final velocity of rod is :

V0 V0 V0
(A) V0 (B) (C) (D)
2 3 4

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38. Total energy loss is
1 1 13
(A) 0 (B) mV02 (C) mV02 (D) mV02
8 3 32
Comprehension-1
A circular conducting loop of radius r0 and having resistance per unit length  is placed in a constant
magnetic field B which is perpendicular to plane of loop. The ends P and Q of the wire are pulled in
opposite directions with a constant speed v such that loop always remains circular and the radius of the
loop goes on decreasing, then answer the following questions.
× × × × × ×
B

× × × × × ×

× × × × × ×
v v
P A Q
× × × × × ×
39. Magnitude of the emf induced in the loop as function of time t is :
r vt   vt   vt   3vt 
(A) 2Bv  0   (B) 2Bv r0   (C) 2Bv r0   (D) 2Bv r0 
2   2     2 

40. Current induced in the loop is at t = 0.

Bv 2Bv Bv Bv
(A) (B) (C) (D)
  2 4

Comprehension-2
A conducting wire is bend into a loop as shown in the figure. The segment AOB is parabolic given by the
equation y2 = 2x, while segment BA is a straight line x = 2.

The magnetic field in the region B = -8k tesla and the current in wire is 2A.

41. The torque on the loop will be :

(A) 16 2N  m (B) 16N  m (C) 18 2N  m (D) zero

42. The magnetic field created by the current in the loop at point C will be :
0  0  0 2 
(A)  k (B)  k (C)  k (D) none of these
4 8 

43. If the loop were rotated about the z-axis with an angular speed of 1rad/sec. Then magnitude of emf induced
across the straight segment AC will be
(A) 32V (B) 8V (C) 16V (D) 4V
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44. A charged particle is moving in a circular path in uniform magnetic field with speed v. Match the following.
Column – I Column – II
(A) equivalent current due to motion of (P) is proportional to v.
charged particle
2
(B) Magnetic Moment (Q) is proportional to v
0
(C) Magnetic field at centre of circle due (R) is proportional to v
to motion of charged particle.
(D) radius of circular path (S) None of these.

Column matching type Questions :


Figure shows a semicircular metallic ring placed in a uniform magnetic field B = –B k̂
Column–1 shows potential difference between two points, Column–2 shows velocity of the semicircular ring
Column–3 represents values of potential differences Answer Q.45, Q.46 by appropriately matching the
information given in the three columns of the following table.
Q
y

P R x

Column–1 Column–2 Column–3

A. VP– VQ P. viˆ 1. vBr
B. VQ– VR Q. v ˆj 2. – vBr
C. VP– VR R. viˆ + v ˆj 3. 2vBr

45. Which of the following is/are correctly matched ?

(A) (A)(P)(1) (B) (A)(Q)(1) (C) (A)(R)(2) (D) (A)(R)(3)

46. Which of the following is/are correctly matched ?

(A) (B)(P)(1) (B) (B)(Q)(1) (C) (C)(R)(3) (D) (C)(Q)(3)

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