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

The correct option is B The resistance will be halved and the specific resistance will remain unchanged

$R=\frac{pl}{A}=\frac{pl}{\pi r^2}$
$R^{\prime }=\frac{p2l}{\pi (2r{)}^2}=\frac{R}{2}$
Specific resistance will remain same as it is a material property but remember it depends on temperature.