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?

Let R be the resistance of each lamp. If E is the applied emf, then the current in the circuit $I_1$  is given by

$I_1=\frac{E}{R+(R/2)}=2E/3R$

Current flowing through $L_{2}or{L}_3$ is

$\frac{1}{2}\left[\frac{2E}{3R}\right]=\frac{E}{3R}$

When $L_3$is fused, the whole current flows through $L_{1}and{L}_2.$

Thus, $I_2=E/2R.$ So current through $L_1$ decreases and the current through $L_2$ increases.