An electric bulb rated $50 \mathrm{~W}-200 \mathrm{~V}$ is connected across a $100 \mathrm{~V}$ supply. The…

An electric bulb rated $50 \mathrm{~W}-200 \mathrm{~V}$ is connected across a $100 \mathrm{~V}$ supply. The power dissipation of the bulb is:
  1. $25 \mathrm{~W}$
  2. $12.5 \mathrm{~W}$
  3. $50 \mathrm{~W}$
  4. $100 \mathrm{~W}$

Solution

Rated power \& voltage gives resistance $\begin{aligned} & \mathrm{R}=\frac{\mathrm{V}^2}{\mathrm{P}}=\frac{(200)^2}{50}=\frac{40000}{50} \\ & \mathrm{R}=800 \\ & \mathrm{P}=\frac{\left(\mathrm{V}_{\text {applied }}\right)^2}{\mathrm{R}}=\frac{(100)^2}{800} \\ & \mathrm{P}=12.5 \text { watt } \end{aligned}$

Asked in: JEE Main 2024 (04 Apr Shift 2)

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