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Three electric bulbs of 200 W, 200 W and 400 W are shown in figure. The resultant power of the combination if rated voltage is applied across the combination is $(50 x)$ Watt. Find value of $x$ .

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Detailed Solution

Let resistance of 400 W is R. Then resistance of 200 W will be 2R.
From $P = \frac{V^{2}}{R}, R = \frac{V^{2}}{400}$

Total resistance of the shown circuit will be 2R $∴ P_{n e t} = \frac{V^{2}}{R_{n e t}} = \frac{V^{2}}{2 R} = \frac{V^{2}}{(V^{2} / 200)} = 200 W$

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