A lamp is rated at $240 \mathrm{~V}, 60 \mathrm{~W}$. When in use the resistance of the filament of the lamp…
A lamp is rated at $240 \mathrm{~V}, 60 \mathrm{~W}$. When in use the resistance of the filament of the lamp is 20 times that of cold filament. The resistance of the lamp when not in use is
$54 \Omega$
$60 \Omega$
$50 \Omega$
$48 \Omega$
Solution
When the lamp is in use,
$\begin{aligned}
& \mathrm{R}=\frac{\mathrm{V}^2}{\mathrm{P}}=\frac{240 \times 240}{60}=960 \Omega \\
& \therefore \quad \mathrm{R}=20 \mathrm{R}^{\prime} \Rightarrow \mathrm{R}^{\prime}=\frac{\mathrm{R}}{20}=\frac{960}{20}=48 \Omega
\end{aligned}$