Q. Two electric bulbs rated $P_{1}\ watt\ V\ $volts and $P_{2}$ 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) $\frac{P_{1} + P_{2}}{P_{1}P_{2}}watt$
Explanation
(a) If resistances of bulbs are $R_{1}$ and $R_{2}$ respectively then in parallel
$\frac{1}{R_{P}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} \Rightarrow \frac{1}{\left( \frac{V^{2}}{P_{p}} \right)} = \frac{1}{\left( \frac{V^{2}}{P_{1}} \right)} + \frac{1}{\left( \frac{V^{2}}{P_{2}} \right)}$
$\Rightarrow P_{P} = P_{1} + P_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.