Explanation

(a) Let resistances are $R_{1}$and $R_{2}$,
Then $S = R_{1} + R_{2}$
And $P = \frac{R_{1}R_{2}}{R_{1} + R_{2}}\ $
$\therefore\left( R_{1} + R_{2} \right) = \frac{n \times R_{1}R_{2}}{R_{1} + R_{2}}\ (From\ S = nP)$
$\Longrightarrow \left( R_{1} + R_{2} \right)^{2} = {nR}_{1}R_{2}$
$\Longrightarrow n = \left\lbrack \frac{R_{1}^{2} + R_{2}^{2} + 2R_{1}R_{2}}{R_{1}R_{2}} \right\rbrack$
$\ \ \ \ \ \ \ \ \ \ = \left\lbrack \frac{R_{1}}{R_{2}} + \frac{R_{2}}{R_{1}} + 2 \right\rbrack$
We know,
Arithmetic Mean $\geq$ Geometric Mean
$\frac{\frac{R_{1}}{R_{2}} + \frac{R_{2}}{R_{1}}}{2} \geq \sqrt{\frac{R_{1}}{R_{2}} \times \frac{R_{2}}{R_{1}}}$
$\Longrightarrow \frac{R_{1}}{R_{2}} + \frac{R_{2}}{R_{1}} \geq 2$
So, n(minimum value) =2+2=4