Question

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

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

Answer 1

Answer: (B)

Resistance of wire $=\rho \frac{l}{A}$
$R\propto \frac{l}{A}=\frac{l}{\pi r^2}$
When length and radius are both doubled
$R_1\propto \frac{2l}{\pi (2r{)}^2}$
$\Rightarrow R_1\propto \frac{1}{2}R$
The specific resistance of wire is independent of geometry of the wire, it only depends on the material of the wire.