Question

$n$ identical resistors each of resistance $r$ when connected in parallel, have a total resistance $R$. When these resistors are connected in series, then effective resistance in terms of $R$ is

• A. $\frac{R}{n^2}$
• B. $n^{2}R$
• C. $nR$
• D. $\frac{R}{n}$

Answer 1

Answer: (B)

When $n$ identical resistors are connected in parallel, the effective resistance is

$R=\frac{r}{n}$ ... (i)
When connected in series, the effective resistance is
$R^{\prime }=nr$ ... (ii)
From Eqs. (i) and (ii), we get
$R^{\prime }=n\times Rn$
$\Rightarrow R^{\prime }=R{n}^2$