Question

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

• A. 4
• B. 3
• C. 2
• D. 1

Answer 1

Answer: (A)

Let resistances be $R_1$ and $R_2$
So, $S = R_1 + R_2$;
$P = \frac{R_{1}R_{2}}{R_{1}+R_{2}}$
$S = nP$
$R_{1}+R_{2} = \frac{nR_{1}R_{2}}{R_{1}+R_{2}}$
$\left(R_{1}+R_{2}\right)^{2} = nR_{1}R_{2}$
If $R_{1} = R_{2}$, so minimum value of $n = 4.$