Question

The above figure shows two resistors X and Y connected in series to a battery. The power dissipated for this combination is \(P_1\). When these resistors 2 are connected in parallel to the same battery then the power dissipated is given by \(P_2\). Find out the ratio \(\frac{P_1}{P_2}\)

Answer 1

For series total resistance is R+2R = 3R 

\(P_1 = \frac{V^2}{3R}\).

For parallel total Resistance is \(\frac{2R}{3}\).

\(P_2 = \frac{V^2}{2R/3} = \frac{3V^2}{2R}\).

\(\frac{P_1}{P_2} = \frac{2}{9}\)