Question

The resultant resistance of $n$ wires each of $r\Omega$ is $R$ when they are connected in parallel. When these wires are connected in series, the resultant resistance will be -

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

Answer 1

The correct option is D $n^{2}R$

When wires are in parallel,

$R=\frac{r}{n}$

$\Rightarrow r=nR$

When they are connected in series,

$R_{\text{eq}}=nr$

$\Rightarrow R_{\text{eq}}=n\times nR$

$\Rightarrow R_{\text{eq}}=n^{2}R$

Hence, option $\left(D\right)$ is the correct answer.