Question

The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then

• A. the resistance and the specific resistance, will both remain unchanged
• B. the resistance will be doubled and the specific resistance will be halved
• C. the resistance will be halved and the specific resistance will remain unchanged
• D. the resistance will be halved and the specific resistance will be doubled

Answer 1

Answer: (C)

$R_1=\frac{\rho {\ell }_1}{A_1},$ now ${\ell }_2=2{\ell }_1$ and $r_2=2r_1$
$A_1=\pi r_1^2$
$A_2=\pi {\left(r_2\right)}^2=\pi {\left(2r_1\right)}^2=4\pi r_1^2=4A_1$
$R_2=\frac{\rho {\ell }_2}{A_2}$
$\therefore R_2=\frac{\rho \left(2{\ell }_1\right)}{4A_1}=\frac{\rho {\ell }_1}{2A_1}=\frac{R_1}{2}$
$\therefore$ Resistance is halved, but specific resistance remains the same.