Question

If a wire of resistance $10\Omega$ is cut along its length such that its diameter becomes half then what will be the new resistance?

• A. $20\Omega$
• B. $30\Omega$
• C. $40\Omega$
• D. $60\Omega$

Answer 1

The correct option is C $40\Omega$

$\frac{R_1}{R_2}=(\frac{d_2}{d_1}{)}^2\Rightarrow \frac{10}{R_2}=(\frac{\frac{d}{2}}{d}{)}^2=\frac{1}{4}$
$\frac{10}{R_2}=\frac{1}{4}\Rightarrow R_2=40\Omega$