The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then:
The electric resistance of a certain wire of iron is $R$. If its length and radius are both doubled, then:
the resistance will be doubled and the specific resistance will be halved
the resistance will be halved and the specific resistance will remain unchanged
the resistance will be halved and the specific resistance will be doubled
the resistance and the specific resistance, both will remain unchanged
Solution
Resistance of wire $R=\rho \frac{l}{A}$ Means $R \propto \frac{l}{A}=\frac{l}{\pi r^2}$
According to the question when $l$ and $R$ are doubled
$\begin{aligned}
& \therefore R_1 \propto \frac{2 l}{\pi(2 r)^2} \\
& \Rightarrow R_1 \propto \frac{1}{2} R
\end{aligned}$
Here specific resistance of wire is independent of geometry wire so it depends on the material of wire.