The resistance of the series combination of two resistances is $S$. When they are joined in parallel through…
The resistance of the series combination of two resistances is $S$. When they are joined in parallel through total resistance is $P$. If $S=n P$, then the minimum possible value of $n$ is
4
3
2
1
Solution
Let resistances be $R_1$ and $R_2$
So, $S=R_1+R_2$;
$
\begin{aligned}
& \mathrm{P}=\frac{\mathrm{R}_1 \mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2} \\
& \mathrm{~S}=\mathrm{nP} \\
& \mathrm{R}_1+\mathrm{R}_2=\frac{\mathrm{nR}_1 \mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2} \\
& \left(\mathrm{R}_1+\mathrm{R}_2\right)^2=\mathrm{nR}_1 \mathrm{R}_2
\end{aligned}
$
If $R_1=R_2$, so minimum value of $n=4$