Question

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

Answer 1

Answer: 4

$R_1+R_2=s\dots (1)$
$\frac{R_1{R}_2}{R_1+R_2}=p$
$R_1{R}_2=sp$
$R_1{R}_2=n{p}^2$
$R_1+R_2=\frac{n{R}_1{R}_2}{\left(R_1+R_2\right)}$
$\frac{{\left(R_1+R_2\right)}^2}{R_1{R}_2}=n$
for minimum value of $n$
$R_1=R_2=R$
$\therefore n=\frac{(2R{)}^2}{R^2}=4$