Question

The equivalent resistance of series combination of two resistors is $'s'$. When they are connected in parallel, the equivalent resistance is $'p'$. If $s = np$, then the minimum value for $n$ is _______ . (Round off to the Nearest Integer)

Answer 1

$R _{1}+ R _{2}= s \ldots(1)$
$\frac{ R _{1} R _{2}}{ R _{1}+ R _{2}}= p$
$R _{1} R _{2}= sp$
$R _{1} R _{2}= np ^{2}$
$R _{1}+ R _{2}=\frac{ nR _{1} R _{2}}{\left( R _{1}+ R _{2}\right)}$
$\frac{\left( R _{1}+ R _{2}\right)^{2}}{ R _{1} R _{2}}= n$
for minimum value of $n$
$R _{1}= R _{2}= R$
$\therefore n =\frac{(2 R )^{2}}{ R ^{2}}=4$