Question

A long resitance wire is divided into 2n parts, n-parts are connected in series and the other n-parts in parallel separately. Both of these sets are connected to identical supplies. Then ratio of heat-produced in series to parallel combination will be

• A. 1 : 1
• B. 1: n${}^2$
• C. 1: n${}^4$
• D. n${}^2$ : 1

Answer 1

The correct option is B 1: n${}^2$

Series

Power dissipated $=\frac{E^2}{nR}$

Parallel

Power dissipated $=n\times \frac{E^2}{R}=\frac{n{E}^2}{R}$

$\frac{P_1}{P_2}=\frac{\frac{E^2}{nR}}{\frac{n{E}^2}{R}}=\frac{1}{n^2}$