Question

A long wire is divided into 2n parts. Then n parts are connected in series and the other n parts are connected in parallel. Both the combinations are given the same voltage supply. The ratio of heat produced in series to parallel combination will be

• A. 1 : 1
• B. 1 : n²
• C. 1 : n⁴
• D. n² : 1

Answer 1

Answer: (B)

1 : n²

Answer 2

Resistance of each part is r = R/2n

R_series = $\frac{R}{2n}$× n = $\frac{R}{2}$

Heat developed in series combination

= $\frac{V^{2}}{(R/2)}$J/sec

R_parallel = $\frac{r}{n}$= $\frac{R/2n}{n}$= $\frac{R}{2n^{2}}$

Heat produced in parallel combination =$\frac{V^{2}}{\left( R/2n^{2} \right)}$ J/sec

∴ $\frac{H_{series}}{H_{parallel}}$= $\frac{2V^{2}}{R}$× $\frac{R}{2n^{2}V^{2}}$= 1 : n²