Question

When $n$ resistors, each of resistance $R$, are connected in series, the equivalent resistance is ___. When $n$ resistors, each of resistance $R$, are connected in parallel, their equivalent resistance is ___.

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

Answer 1

The correct option is B

$nR,\frac{R}{n}$

When n resistors of resistance R each are connected in series,
$R_{eq}=R+R+R+....+R\left(ntimes\right)$
$=n\times R=nR$
When n resistors of resistance R each is connected in parallel,
$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R}.....+\frac{1}{R}\left(ntimes\right)\frac{1}{R_{eq}}=\frac{n}{R}{R}_{eq}=\frac{R}{n}$