Question

A wire of resistance $10\Omega$ is cut such that its area becomes $\frac{1}{3}$rd. If the length is unchanged then what will be the new resistance?

• A. $20\Omega$
• B. $30\Omega$
• C. $28\Omega$
• D. $32\Omega$

Answer 1

The correct option is B $30\Omega$

Resistance of a wire is inversely proportional to its area.
$\frac{R_1}{R_2}=\frac{A_2}{A_1}\Rightarrow \frac{10}{R_2}=\frac{A/3}{A}=\frac{\frac{A}{3}}{\frac{A}{1}}$
$\frac{10}{R_2}=\frac{A}{3}\times \frac{1}{A}$
$R_2=30\Omega$