2004 AIPMT Current ElectricityResistance and resistivity Easy Question 3 of 3 in Resistance and resistivity

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

The answer is A.

Solution

The specific resistance (resistivity) $\rho$ depends only on the material and its temperature, not on the dimensions. The material is the same (iron), so $\rho$ remains unchanged.
Resistance of a wire: $R = \dfrac{\rho l}{A} = \dfrac{\rho l}{\pi a^2}$, where $a$ is the radius.
So $R \propto \dfrac{l}{a^2}$
New length $= 2l$ and new radius $= 2a$:
$R' \propto \dfrac{2l}{(2a)^2} = \dfrac{2l}{4a^2} = \dfrac{1}{2}\cdot\dfrac{l}{a^2}$
$\Rightarrow R' = \dfrac{R}{2}$
So the resistance will be halved and the specific resistance will remain unchanged.

Concept Dependence of resistance on dimensions

Resistance and resistivity in past papers

3 questions from this chapter have appeared across 3 exam years.