Question

Three bulbs $B_1,B_2$ and $B_3$ are connected to the mains as shown in the figure. How will the brightness of bulb $B_1$ be affected if $B_2$ or $B_3$ are disconnected from the circuit?

• A. Bulb $B_1$ becomes brighter
• B. Bulb $B_1$ becomes dimmer
• C. No change occurs in the brightness
• D. Bulb $B_1$ becomes brighter if bulb $B_2$ is disconnected and dimmer if bulb $B_3$ is disconnected

Answer 1

The correct option is B Bulb $B_1$ becomes dimmer

Let R be the resistance of each bulb connected in this circuit.
The equivalent resistance in this case would be
$R_{eq}=R+\frac{R}{2}$
$R_{eq}=\frac{3R}{2}$

But if one of the bulb (i.e $B_2$ or $B_3$) gets disconnected

The effective resistance would be
$R_{eq}=2R$

Thus, in the later case the resistance gets increased due to which current flowing the circuit will decrease which would ultimately lead to bulb $B_1$ becoming dimmer.