Question

An inductor of inductance $$L = 400 mH$$   and resistors of resistance $${R_1} = 2\Omega $$   and $${R_2} = 2\Omega $$   are connected to a battery of emf $$12\,V$$ as shown in the figure. The internal resistance of the battery is negligible. The switch $$S$$ is closed at $$t = 0.$$  The potential drop across $$L$$ as a function of time is:

A. $$\frac{{12}}{t}{e^{ - 3t}}V$$
B. $$6\left( {1 - {e^{ - \frac{t}{{0.2}}}}} \right)V$$
C. $$12{e^{ - 5t}}V$$  
D. $$6{e^{ - 5t}}V$$
Answer :   $$12{e^{ - 5t}}V$$
Solution :
Growth in current in $$L{R_2}$$  branch when switch is closed is given by
$$i = \frac{E}{{{R_2}}}\left[ {1 - {e^{ - \frac{{{R_2}t}}{L}}}} \right] \Rightarrow \frac{{di}}{{dt}} = \frac{E}{{{R_2}}}.\frac{{{R_2}}}{L}.{e^{ - \frac{{{R_2}t}}{L}}} = \frac{E}{L}{e^{ - \frac{{{R_2}t}}{L}}}$$
Hence, potential drop across
$$\eqalign{ & L = \left( {\frac{E}{L}{e^{ - \frac{{{R_2}t}}{L}}}} \right)L = E{e^{ - \frac{{{R_2}t}}{L}}} = 12{e^{ - \frac{{2t}}{{400 \times {{10}^{ - 3}}}}}} \cr & = 12{e^{ - 5t}}V \cr} $$

Releted MCQ Question on
Electrostatics and Magnetism >> Electromagnetic Induction

Releted Question 1

A thin circular ring of area $$A$$ is held perpendicular to a uniform magnetic field of induction $$B.$$ $$A$$ small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is $$R.$$ When the ring is suddenly squeezed to zero area, the charge flowing through the galvanometer is

A. $$\frac{{BR}}{A}$$
B. $$\frac{{AB}}{R}$$
C. $$ABR$$
D. $$\frac{{{B^2}A}}{{{R^2}}}$$
Releted Question 2

A thin semi-circular conducting ring of radius $$R$$ is falling with its plane vertical in horizontal magnetic induction $$\overrightarrow B .$$  At the position $$MNQ$$  the speed of the ring is $$v,$$ and the potential difference developed across the ring is
Electromagnetic Induction mcq question image

A. zero
B. $$\frac{{Bv\pi {R^2}}}{2}$$  and $$M$$ is at higher potential
C. $$\pi RBv$$  and $$Q$$ is at higher potential
D. $$2RBv$$  and $$Q$$ is at higher potential
Releted Question 3

Two identical circular loops of metal wire are lying on a table without touching each other. Loop-$$A$$ carries a current which increases with time. In response, the loop-$$B$$

A. remains stationary
B. is attracted by the loop-$$A$$
C. is repelled by the loop-$$A$$
D. rotates about its $$CM,$$  with $$CM$$  fixed
Releted Question 4

A coil of inductance $$8.4 mH$$  and resistance $$6\,\Omega $$  is connected to a $$12 V$$  battery. The current in the coil is $$1.0 A$$  at approximately the time

A. $$500 s$$
B. $$25 s$$
C. $$35 ms$$
D. $$1 ms$$

Practice More Releted MCQ Question on
Electromagnetic Induction


Practice More MCQ Question on Physics Section