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 $r=R/2n$


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


$R_{p a r a l l e l}=\frac{r}{n}= \, \frac{R / 2 n}{n}= \, \frac{R}{2 n^{2}}$
The heat produced in parallel combination $=\frac{V^{2}}{\left(R / 2 n^{2}\right)} \, Js^{- 1}$



$\therefore \, \frac{H_{s e r i e s}}{H_{p a r a l l e l}}= \, \frac{2 V^{2}}{R}\times \, \frac{R}{2 n^{2} V^{2}}= \, 1:n^{2}$