Three identical bulbs, each rated 60 W, 200 V, are connected in series to a 200 V supply. The total power drawn by them is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20 W
A bulb rated \( P \) at voltage \( V \) has resistance \( R=V^2/P \), which stays the same in the new circuit. In series the resistances add, and the power drawn from the supply is \( V^2/R_{\mathrm{eq}} \).
The resistance of each bulb is:
\( \begin{aligned} R &= \frac{V^2}{P} \\ &= \frac{(200\,\mathrm{V})^2}{60\,\mathrm{W}} \\ &= \frac{2000}{3}\,\Omega \end{aligned} \)
The three bulbs in series give:
\( \begin{aligned} R_{\mathrm{eq}} &= 3R \\ &= 3\times\frac{2000}{3}\,\Omega \\ &= 2000\,\Omega \end{aligned} \)
The total power drawn from the 200 V supply is:
\( \begin{aligned} P_{\mathrm{total}} &= \frac{V^2}{R_{\mathrm{eq}}} \\ &= \frac{(200\,\mathrm{V})^2}{2000\,\Omega} \\ &= 20\,\mathrm{W} \end{aligned} \)