Question

When n resistors of resistance R each is connected in series, the effective resistance is ___ and when they are connected in parallel, their effective resistance is ___.

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

Answer 1

The correct option is B $n\times R,\frac{R}{n}$

When n resistors of resistance R each is connected in series,
$R_{e}q=R_1+R_2+R_3+........+R_n\left(ntimes\right)=n\times R=nR$
When n resistors of resistance R each is connected in parallel,
$\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R_n}.....\frac{1}{R_{eq}}=\frac{n}{R}Req=\frac{R}{n}$