Question

The resistance of the series combination of two resistors is $S.$ When they are joined in parallel the equivalent resistance becomes $P.$ . If $S=nP,$ then the minimum possible value of $n$ is

Answer 1

Answer: 4

In series combination, $S=\left(R_1+R_2\right)$
In series combination $P=\frac{R_1{R}_2}{\left(R_1+R_2\right)}$
$\because S=nP$
$\therefore \left(R_1+R_2\right)=n\frac{R_1{R}_2}{\left(R_1+R_2\right)}$
$\therefore {\left(R_1+R_2\right)}^2=n{R}_1{R}_2$
For minimum value, $R_1=R_2=R$
$(R+R=n(R\times R)\Rightarrow 4R^2=n{R}^2\Rightarrow n=4$