Question

A wire of resistance R is cut into n equal parts these parts are then connected in parallel with each other. The equivalent resistance of the combination is :

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

Answer 1

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

when wire of resistance R is cut into n equal parts then Resistance of each part will be $\frac{R}{n}$;

such $n$ parts are joined in parallel

$\frac{1}{R_{eq}}=$$\frac{1}{\left(R/n\right)}+$$\frac{1}{\left(R/n\right)}+$$\frac{1}{\left(R/n\right)}+$$\frac{1}{\left(R/n\right)}+$...

so $R_{eq}=\frac{R}{n^2}$.