Question

Figure shows three similar lamps $L_1$, $L_2$, and $L_3$ connected across a power supply. If the lamp $L_3$ fuses, how will the light emitted by $L_1$ and $L_2$ change?

• A. no change
• B. brilliance of $L_1$ decreases and that of $L_2$ increases
• C. brilliance of both $L_1$ and $L_2$ increases
• D. brilliance of both $L_1$ and $L_2$ decreases

Answer 1

The correct option is B brilliance of $L_1$ decreases and that of $L_2$ increases

Let R be the resistance of each lamp. If E is the applied emf.

The total resistance of the circuit is $R_t=R+R||R=R+\frac{RR}{R+R}=R+R/2=3R/2$

Current in the circuit is $I=E/R_t=2E/3R$

As $L_2$ and $L_3$ are parallel and have identical resistance so total

current $I$ is equally divided into two branch. Thus, current through

$L_2$ or $L_3$ is $I/2$

When $L_3$ is fused, total resistance becomes $R_t^{\prime }=R+R=2R$ and

current $I^{\prime }=E/2R$. Now this is the current through $L_1$ and $L_2$.

Thus, the current through $L_1$ decreases and current through $L_2$ increases.