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 the parallel combination will be

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

Answer 1

Answer: (B)

The resistance of each part is $r=R/2n$


$R_{series}=\frac{R}{2n}\times n=\frac{R}{2}$
The heat developed in series combination
$=\frac{V^2}{\left(R/2\right)}J{s}^{-1}$


$R_{parallel}=\frac{r}{n}=\frac{R/2n}{n}=\frac{R}{2n^2}$
The heat produced in parallel combination $=\frac{V^2}{\left(R/2n^2\right)}J{s}^{-1}$



$\therefore \frac{H_{series}}{H_{parallel}}=\frac{2V^2}{R}\times \frac{R}{2n^2{V}^2}=1:n^2$