Question

The resistance of $n$ wires each of resistance $rohms$ is $R$, when they are connected in parallel. When these resistance 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 $n^{2}R$

It is given that, resistance of n wires each of resistance r ohm is R when they are connected in parallel. So,

$\frac{1}{r}+\frac{1}{r}+\frac{1}{r}........ntimes=\frac{1}{R}$

$\frac{n}{r}=\frac{1}{R}$

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

When resistors are connected in series, the equivalent resistance will be,

$r+r+r+r...........ntimes=nr$

$=n\left(nR\right)=n^{2}R$