Question

An inductor $L$, a resistance $R$ and two identical bulbs $B_1$ and $B_2$ are connected to a battery through a switch $S$ as shown in the figure. The resistance of coil having inductance $L$ is also $R$. Which of the following statement gives the correct description of the happenings, when the switch $S$ is closed ?

• A. The bulb $B_2$ lights up earlier than $B_1$ and finally both the bulbs shine equally bright.
• B. $B_1$ light up earlier and finally both the bulbs acquire equal brightness.
• C. $B_2$ lights up earlier and finally $B_1$ shines brighter than $B_2$.
• D. $B_1$ and $B_2$ light up together with equal brightness all the time.

Answer 1

The correct option is A The bulb $B_2$ lights up earlier than $B_1$ and finally both the bulbs shine equally bright.

$\Rightarrow$brightness of a bulb $\propto$ (Potential difference across it).
$\because$ Inductor will offer $\infty$ resistance till steady state current is achieved after some times.
$\Rightarrow$Initially the growth of current in the branch containing $B_1$ gets delayed as inductor oppose changes of current, hence it will not light up.

After staedy state is achieved then inductor will offer its normal resistance ($R\Omega$)

$\therefore$ Both parts of circuit become equivalent, so potential difference across bulbs will also be equal. That means brightness of bulbs become same after some time.