Two electric bulbs rated P1 watt V volts and P2 watt V volts are connected in parallel and V volts are applied to it. The total Power will be

Two electric bulbs rated P₁ watt V volts and P₂ watt V volts are connected in parallel and V volts are applied to it. The total Power will be

A
$(P_{1} + P_{2}) watt$
B
$\sqrt{P_{1} + P_{2}} watt$
C
$\frac{P_{1} P_{2}}{P_{1} + P_{2}} watt$
D
$\frac{P_{1} + P_{2}}{P_{1} P_{2}} watt$

Solution:

If resistances of bulbs are R₁ and R₂, respectively, then in parallel $\frac{1}{R_{P}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

$\Rightarrow \frac{1}{(\frac{V^{2}}{P_{p}})} = \frac{1}{(\frac{V^{2}}{P_{1}})} + \frac{1}{(\frac{V^{2}}{P_{2}})} \Rightarrow P_{P} = P_{1} + P_{2}$

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