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

In series combination, $S=\left(R_{1} + R_{2}\right)$
In series combination $P=\frac{R_{1} R_{2}}{\left(R_{1} + R_{2}\right)}$
$\because S=nP$
$\therefore \left(R_{1} + R_{2}\right)=n\frac{R_{1} R_{2}}{\left(R_{1} + R_{2}\right)}$
$\therefore \left(R_{1} + R_{2}\right)^{2}=nR_{1}R_{2}$
For minimum value, $R_{1}=R_{2}=R$
$ \left(R+R=n(R \times R) \Rightarrow 4 R^{2}=n R^{2} \Rightarrow n=4\right. $