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)

The resistance will be halved and the specific resistance will remain unchanged

Answer 2

Material same $\Rightarrow \rho$ unchanged
$R =\frac{\rho \ell}{ A }=\frac{\rho \ell}{\pi a ^{2}}$
$\Rightarrow R \propto \frac{\ell}{ a ^{2}}$
therefore $R ' \propto \frac{2 \ell}{(2 a )^{2}}$
$\Rightarrow R ' =\frac{ R }{2}$