Question

A, B, C are three identical lamps connected as shown in the following fig. What changes occur in the brightness of the lamps when switch S is closed?

• A. Brightness of A increases but that of B decreases.
• B. Brightness of A remains same but that of B decreases.
• C. Brightness of a increase but that of B remains same.
• D. Brightness of both A and B decreases.

Answer 1

The correct option is A Brightness of A increases but that of B decreases.

Assuming all bulbs are identical with resistance, $R$ and the voltage across battery terminals is $V$ volts.
In order to infer the change in brightness of the bulbs we need to look at the change in current through them. An increase in current will lead to increase in brightness and decrease in current will lead to reduction in brightness.
Initially, when switch S is open, total equivalent resistance of the circuit, $R_{eq}=2R$ and
current flowing through bulbs A and B is same and is equal to, $I_1=\frac{V}{2R}$.
When the switch S is closed, total equivalent resistance of the circuit, $R_{eq}=1.5R$ and
current flowing through bulbs A will be, $I_A=\frac{2V}{3R}$,
current flowing through bulb B will be, $I_B=\frac{I_A}{2}=\frac{V}{3R}$.

Thus, current flowing through A has increased from $\frac{V}{2R}$ to $\frac{2V}{3R}$ that leads to an increase in brightness
and current flowing through B has decreased from $\frac{V}{2R}$ to $\frac{V}{3R}$ that leads to a decrease in brightness.