Question

A certain wire has resistance $R$. The resistance of another wire identical with the first except having twice its diameter is:

• A. $2R$
• B. $0.25R$
• C. $4R$
• D. $0.5R$

Answer 1

The correct option is B $0.25R$

Resistance is inversely proportional to the cross sectional area

$\begin{array}{c}R\propto \frac{1}{A}\\ \propto \frac{1}{\frac{\pi d^2}{4}}\\ \propto \frac{1}{d^2}\\ \frac{R^{\prime }}{R}={\left(\frac{d}{d^{\prime }}\right)}^2\\ R^{\prime }=R{\left(\frac{d}{d^{\prime }}\right)}^2=\frac{R}{4}=0.25R\end{array}$