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. $ n\,R $
• 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
$R'=n r$ ... (ii)
From Eqs. (i) and (ii), we get
$R' =n \times R n$
$\Rightarrow R' =R n^{2}$