STD:XI Advance Date - M.

Prakash Institute
Section I - Single Option correct - 22 questions

1. A mutual inductor consists of two coils X and Y as shown in figure in which one-
quarter of the magnetic flux produced by X links with Y , giving a mutual inductance
M . What will be the mutual inductance when Y is used as the primary?

(A) M/4 (B) M/2 (C) M (D) 2M

2. A coil carrying a steady current is short-circuited. The current in it decreases α

times in time t0◦ . The time constant of the circuit is
t0 t0 t0
(A) τ = t0 ln α (B) τ = ln α
(C) τ = α
(D) τ = α−1

3. A solenoid has 2000 turns wound over a length of 0.3 m. Its cross-sectional area
is equal to 1.2 × 10−3 m2 . Around its central cross-section a coil of 300 turns is
wound. If an initial current of 2 A flowing in the solenoid is reversed in 0.25 s, the
emf induced in the coil is
(A) 0.6 mV (B) 60 mV (C) 48 mV (D) 0.48 mV

4. The time constant of an inductance coil is 2 × 10−3 s. When a 90 − Ω resistance

is joined in series, the same constant hecomes 0.5 × 10−3 s. The inductance and
resistance of the coil are
(A) 30mH; 30Ω (B) 60mH; 30Ω (C) 30mH; 60Ω (D) 60mH; 60Ω

5. The coefficient of mutual inductance of two circuits A and B is 3 mII and their
respective resistances are 10 and 4 Ω. How much current should change in 0.02 s in
circuit A, so that the induced current in B should be 0.0060 A ?
(A) 0.24 A (B) 1.6 A (C) 0.18 A (D) 0.16 A

6. An emf of 15 V is applied in a circuit containing 5H inductance and 10Ω resistance.

The ratio of the currents at time t = ∞ and t = 1 s is
e1/2 e2
(A) e1/2 −1
(B) e2 −1
(C) 1 − e−1 (D) e−1

7. A current i0 is flowing through an L − R circuit of time constant t0 . The source of

the current is switched off at time t = 0. Let r be the value of (−di/dt) at time
t = 0. Assuming this rate to be constant, the current will reduce to zero in a time
interval of
 
t0 1
(A) t0 (B) et0 (C) e
(D) 1 − e
t0

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 8. A small coil of radius r is placed at the center of a large coil of radius R, where
R >> r. The two coils are coplanar. The mutual inductance between the coils is
proportional to
(A) r/R (B) r2 /R (C) r2 /R2 (D) r/R2

9. The length of a wire required to manufacture a solenoid of length l and self induc-
tion L is (cross-sectional arca is negligible)
q q q q
2πL.l µ0 LI 4πLl µ0 Ll
(A) µ0
(B) 4π
(C) µ0
(D) 2π

10. A toroid is wound over a circular core. Radius of each turn is r and radius of toroid
is R(> r). The coefficient of selfinductance of the toroid is given by

µ0 N r 2 µ0 N r µ0 N r2 µ0 N 2 r 2
(A) L = 2R
(B) L = 2R
(C) L = R
(D) L = 2R

11. In figure, the mutual inductance of a coil and a very long straight wire is M , the
coil has resistance R and self-inductance L. The current in the wire varies according
to the law i = at, where a is a constant and t is the time, the time dependence of
current in the coil is

 
(A) M
aR
(B) M aRe−RvL (C) M −tR/L
R
e (D) Ma
R
1 − e−tR/L

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12. In the circuit shown (figure), X is joined to Y for a long time and then X is joined
to Z. The total heat produced in R2 is

LE 2 LE 2 LE 2 LE 2 R2
(A) 2R12
(B) 2R22
(C) 2R1 R2
(D) 2R13

13. Figure shows a rectangular coil near a long wire. The mutual inductance of the
combination is

       
µ0 a b µ0 a b µ0 a b µ0 a b
(A) 2π
ln 1 − c
(B) 2π
ln 1 + c
(C) π
ln 1 + c
(D) √
2π
ln 1 + c

14. In the circuit shown (figure), the cell is ideal. The coil has an inductance of 4 H
and zero resistance. F is a fuse of zero resistance and will blow when the current
through it reaches 5 A. The switch is closed at t = 0. The fuse will blow

(A) almost at once (B) after 2 s (C) after 5 s (D) after 10 s

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15. In the circuit shown in figure, switch S is closed at time t = 0. The charge that
passes through the battery in one time constant is

 
eR2 E L EL eL
(A) L
(B) E R
(C) eR2
(D) ER

16. Switch S shown in figure is closed for t < 0 and is opened at t = 0. When currents
through L1 and L2 are equal, their common value is

E E(L2 +L1 ) EL1 E (L1 +L2 )

(A) R
(B) RL1
(C) R(L1 +L2 )
(D) R L2

17. Given L1 = 1mH, R1 = 1Ω, L2 = 2mH, R2 = 2Ω

Neglecting mutual inductance, the time constants (in ms) for circuits (i), (ii), and
(iii) are
(A) 1, 1, 92 (B) 94 , 1, 1 (C) 1, 1, 1 (D) 1, 94 , 1

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18. Two resistors of 10Ω and 20Ω and an ideal inductor of 10H are connected to a 2 V
battery as shown in figure. Key K is inserted at time t = 0. The initial (t = 0) and
final (t → ∞) currents through the battery are

1 1 1 1 2 1 1 2
(A) 15
A, 10 A (B) 10
Λ, 15 A (C) 15
A, 10 A (D) 15
A, 25 A

19. A square conducting loop of side L is situated in gravity-free space. A small con-
ducting circular loop of radius r(r ≪ L) is placed at the center of the square loop,
with its plane perpendicular to the plane of the square loop. The mutual inductance
of the two coils is
√ √
2 2µ0 I 2 2µ0 I0 2
(A) L
r (B) L
r (C) 0 (D) none of these

20. A bulb of 100 W is connected in parallel to an ideal inductance of 1H. This ar-
rangement is connected to a 90 V battery through a switch. On pressing the switch
the
(A) bulb does not glow
(B) bulb glows
(C) bulb glows after a short time and then continues to glow
(D) bulb glows for a short time and then stops glowing.

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21. The diagram given below shows a solenoid carrying time varying current l = l0 t.
On the axis of the solenoid, a ring has been placed. The mutual inductance of the
ring and the solenoid is M and the self inductance of the ring is L. If the resistance
of the ring is R then maximum current which can flow through the ring is

(2M +L)l0 M I0 (2M −L)I0 (M +L)I0

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

22. An inductor resistance battery circuit is switched on at t = 0. If the emf of the

battery is E, find the charge which passes through the battery during one timé
constant τ .
E τ E τ E τ E (e−1)
(A) R
· e
(B) R
· (e−1)
(C) R
· (e+1)
(D) R
· τ

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 Section II - Multiple Correct Option - 9 questions

23. For the circuit shown in figure, which of the following statements is/are correct?

(A) Its time constant is 0.25 s

(B) In steady state, current through the inductance will be equal to zero
(C) In steady state, current through the battery will be equal to 0.75 A
(D) None of these

24. In the circuit shown in figure, the switch is closed at t = 0.

(A) At t = 0, I1 = I2 = 0
(B) At any time t, II12 = LL21
(C) At any time t, I1 + I2 = Rε
(D) At t = ∞, I1 and I2 are independent of L1 and L2

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25. The potential difference across a 2 − H inductor as a function of time is shown in
figure. At t = 0, current is zero. Choose the correct statement.

(A) Current at t = 2 s is 5 A
(B) Current at t = 2 s is 10 A
(C) Current versus time graph across the inductor will be [Figure (a)]
(D) Current versus time graph across inductor will be [Figure (b)]

26. Two parallel resistanceless rails are connected by an inductor of inductance L at

one end as shown in figure. A magnetic field B exists in the space which is perpen-
dicular to the plane of the rails. Now a conductor of length l and mass m is placed
transverse on the rail and given an impulse J toward the rightward direction. Then
choose the correct option(s).

(A) Velocity of theqconductor is half of the initial velocity after a displacement of

2
the conductor d = 4B3J2 l2Lm
(B) Current flowing through the inductorqat the instant when velocity of the con-
3J 2
ductor is half of the initial velocity is i = 4Lm
(C) Velocity of theqconductor is half of the initial velocity after a displacement of
2
the conductor d = B3J2 l2Lm
(D) Current flowing through the inductorqat the instant when velocity of the con-
2
ductor is half of the initial velocity is i = 3J
mL

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27. In the circuit, a battery of emf E, a resistance R and inductance coil L1 and L2 and
switch S are connected as shown. in figure. Initially the switch is open

 
(A) The time constant of the circuit is R1 LL11+L
L2
2
(B) Steady state current in the inductor L1 is R(LEL 2
1 +L2 )

(C) Steady state, current in the inductor L2 is R(LEL 1

1 +L2 )  
1 L1 L2 E2
(D) In steady state the total energy stored in the inductor coils is 2 L1 +L2 R2

28. When current ( I ) in R − L series circuit becomes constant, where L is a pure

inductor, which of the following given statements is/are correct?

(A) voltage across R is RI.

(B) some part (not 100% ) of the energy supplied by the battery will be dissipated
in R and remaining will continue to store in L.
(C) voltage across L is equal to zero
(D) magnetic energy stored is 12 LI 2

29. A time varying voltage V = 2t (Volt) is applied across an ideal inductor of induc-
tance L = 2H as shown in figure.
Then (assume current to be zero at t = 0 )

(A) current versus time graph is a parabola

(B) energy stored in magnetic field at t = 2 s is 4 J
(C) potential energy at time t = 1 s in magnetic field is increasing at a rate of 1 J/s
(D) energy stored in magnetic field is zero all the time

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30. In the circuit shown in figure, circuit is closed at time t = 0. At time t = ln(2)
second:

(A) Rate of energy supplied by the battery is 16 J/s

(B) Rate of heat dissipated across resistance is 16 J/s
(C) Rate of heat dissipated across resistance is 8 J/s
(D) Va − Vh = 2V

31. The current growth in two L − R circuits (b) and (c) is as shown in Fig. (a). Let
L1 , L2 , R1 , and R2 be the corresponding values in two circuits. Then

(A) R1 > R2 (B) R1 = R2 (C) L1 > L2 (D) L1 < L2

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 Section III - Numerical - 7 questions

32. In the circuit (figure) what is potential difference VB − VA (in V ) when current I
is 5 A and is decreasing at the rate of 103 A s−1 ?

33. A current of 2 A is increasing at a rate of 4 A s−1 through a coil of inductance 1 H.

Find the energy stored in the inductor per unit time in the units of Js−1 .

34. Two coils, 1 and 2 have a mutual inductance M = 5 H and resistance R = 10Ω
each. A current flows in coil 1 , which varies with time as: I1 = 2t2 , where t is time.
Find the total charge (in C ′ ) that has flown through coil 2 between t = 0 and t = 2 s.

35. A long solenoid of diameter 0.1 m has 2 × 104 turns per metre. At the center of the
solenoid, a 100 -turn coil of radius 0.01 m is placed with its axis coinciding with the
solenoid axis. The current in the solenoid is decreased at a constant rate from +2 A
to −2 A in 0.05 s. Find the total charge (in µC ) flowing through the coil during
this time when the resistance of the coil is 40π 2 Ω.

36. Figure shows a circuit having a coil of resistance R = 2.5Ω and inductance L
connected to a conducting rod P Q which can slide on a perfectly conducting circular
ring of radius 10 cm with its center at P .

Assume that friction and gravity are absent and a constant uniform magnetic field
of 5 T exists as shown in figure. At t = 0, the circuit is switched on and simultane-
ously a time-varying external torque is applied on the rod so that it rotates about
P with a constant angular velocity 40rads−1 . Find the magnitude of this torque (in
mNm ) when current reaches half of its maximum value. Neglect the self inductance
of the loop formed by the circuit.

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37. In the given circuit, what is the current I (in A) drawn from battery at time t = 0.

38. A certain volume of copper is drawn into a wire of radius a and is wrapped in
shape of a helix having radius r(>> a). The windings are as close as possible
without overlapping. Self-inductance of the inductor so obtained is L1 . Another
wire of radius 2a is drawn using same volume of copper and wound in the fashion
as described above. This time the inductance is L2 . Find LL12 .

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Answer Key:
Q. No Ans Q.No. Ans Q.No. Ans Q.No Ans Q.No Ans
1 C 9 C 17 A 25 AC 33 8.00
2 B 10 D 18 A 26 AB 34 4.00
3 C 11 D 19 C 27 ABCD 35 8.00
4 B 12 A 20 D 28 ACD 36 5.00
5 D 13 B 21 B 29 ABC 37 1.00
6 B 14 D 22 A 30 AC 38 8.00
7 A 15 C 23 AC 31 BD
8 B 16 C 24 AB 32 8.00

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