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Q.

Two identical heaters rated 220V, 1000 W are placed in series with each other across 220 volt line; then the equivalent combined power in the circuit is

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a

2000 W

b

1000 W

c

500 W

d

4000 W

answer is C.

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Detailed Solution

$\begin{array}{l} P_{1} = \frac{V^{2}}{R_{1}} \Rightarrow R_{1} = \frac{V^{2}}{P_{1}} Similarly R_{2} = \frac{V^{2}}{P_{2}} and R_{eff} = \frac{V^{2}}{P_{eff}} \\ R_{s} = R_{1} + R_{2} \Rightarrow \frac{V^{2}}{P_{eff}} = \frac{V^{2}}{P_{1}} + \frac{V^{2}}{P_{2}} \end{array}$

$\Rightarrow \frac{1}{P_{eff}} = \frac{1}{P_{1}} + \frac{1}{P_{2}} here P_{1} = 1000 W, P_{2} = 1000 W So, P_{eff} = 500 W$

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