Question

Two electric bulbs rated P${}_1$ watt V volts and P${}_2$ watt V volts are connected in parallel and applied across V volts. The total power (in watt) will be

• A. $P_1+P_2$
• B. $\sqrt{P_1{P}_2}$
• C. $\frac{P_1{P}_2}{P_1+P_2}$
• D. $\frac{P_1+P_2}{P_1{P}_2}$

Answer 1

The correct option is A $P_1+P_2$

Resistance of 1st bulb$R_1=\frac{V^2}{P_1}$ & Resistance of 2nd bulb$R_2=\frac{V^2}{P_2}$

In parallel mode equivalent resistance$R_{eq.}=\frac{R_1\times R_2}{R_1+R_2}$

Power output(P)=$P=\frac{V^2}{R_{eq.}}P=\frac{\frac{V^2}{1}}{\left(\frac{\left(\frac{V^2}{P_1}\right)\times \left(\frac{V^2}{P_2}\right)}{\frac{V^2}{P_1}+\frac{V^2}{P_2}}\right)}P=\left(V^2\right)\times \left(\frac{\frac{V^2}{P_1}+\frac{V^2}{P_2}}{(\frac{V^2}{P_1}\times \frac{V^2}{P_2})}\right)$

$\Rightarrow \frac{\frac{1}{P_1}+\frac{1}{P_2}}{\frac{1}{P_1{P}_2}}$

$\Rightarrow P_1+P_2$