Question

Three Identical bulbs $B_1,B_2$ and $B_3$ are connected to voltage $V$ as shown below. When the switch $S$ is closed

• A. Brightness of $B_2$ will increase
• B. Brightness of $B_1$ will decrease
• C. Brightness of $B_3$ will decrease
• D. Brightness of $B_1$ will increase

Answer 1

The correct option is D Brightness of $B_1$ will increase

Let $R$ be the resistance of each bulb.
(I) When the switch is not closed:
Equivalent resistance of the circuit is:
$R_{eq}=R+R=2R$

(II) When the switch is closed:
The equivalent resistance across $B_2$ and $B_3$ is reduced.
$\therefore R_{23}=\frac{R\times R}{R+R}=\frac{R}{2}$
Total equivalent resistance will also decrease.

$\therefore R_{eq}=R+\frac{R}{2}=\frac{3R}{2}$
Current $l\propto \frac{1}{\text{Resistance}}$
Thus, current through bulb $B_1$ will increase, and hence, the brightness of bulb $B_1$ will increase when the switch is closed.
Hence, the correct answer is option (d).