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 $r_{2}=2r_{1}$
$A_{1}=\pi r^{2}_{1}$
$A_{2}=\pi\left(r_{2}\right)^{2}=\pi\left(2r_{1}\right)^{2}=4\pi r^{2}_{1}=4A_{1}$
$R_{2}=\frac{\rho \ell _{2}}{A_{2}}$
$\therefore \:R_2=\frac{\rho \left(2\ell _1\right)}{4A_1}=\frac{\rho \ell _1}{2A_1}=\frac{R_1}{2}$
$\therefore $ Resistance is halved, but specific resistance remains the same.