A torch bulb rated as $4.5\, W, 1.5\, V$ is connected as shown in the figure. The $e.m.f.$ of the cell needed to make the bulb glow at full intensity is ............. $V$
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Resistance of bulb is
$\frac{1.5 \times 1.5}{4.5} \Omega=0.5 \Omega$
Resistance of parallel combination,
$R=\frac{1 \times \frac{1}{2}}{1+\frac{1}{2}} \Omega=\frac{1}{3} \Omega$
Now, $r=\frac{E-V}{V} R$ or $\frac{8}{3}=\frac{E-1.5}{1.5} \times \frac{1}{3}$ or $E=13.5 \mathrm{V}$
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