Question

The resultant resistance of $n$ wires each of resistance $r\text{ohms}$ is $R$, when they are connected in parallel. When these $n$ resistances 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 $n^{2}R$



Each wire have resistance of $r$ and connected in parallel.
So equivalent resistance of above circuit will be

$\frac{1}{R_{eq}}=\frac{1}{r}+\frac{1}{r}+....n\text{times}$

$\frac{1}{R}=\frac{n}{r}(\text{given,}{R}_{eq}=R)$

$\therefore r=nR..........\left(1\right)$

For series combination:


$R_{eq}^{\prime }=r+r+r+....n\text{times}$

From equation $\left(1\right)$,

$R_{eq}^{\prime }=nr=n\left(nR\right)=n^{2}R$

Hence, option $\left(d\right)$ is the right choice.