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Q.

Two electric bulbs rated $P_{1}$ watt V volts and $P_{2}$ watt V volts are connected in series and V volts are applied to it. The total power will be

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a

$P_{1} + P_{2} w a t t$

b

$\frac{P_{1} P_{2}}{P_{1} + P_{2}} w a t t$

c

$\sqrt{P_{1} P_{2}} w a t t$

d

$\frac{\sqrt{P_{1} P_{2}}}{P_{1} + P_{2}} w a t t$

answer is D.

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Detailed Solution

$R_{1} = \frac{V^{2}}{P_{1}} a n d R_{2} = \frac{V^{2}}{P_{2}}$

$P_{c o n s u m e d} = \frac{V^{2}}{R_{1} + R_{2}} = \frac{V^{2}}{(\frac{V^{2}}{P_{1}} + \frac{V^{2}}{P_{2}})} = (\frac{P_{1} P_{2}}{P_{1} + P_{2}})$

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