Question

The resistance of a conductor is proportional to
(A) length
(B) radius
(C) cross section
(D) none of the above

Answer 1

Hint:Use the formula of the resistivity given below and rearrange it to find the relation between the resistance and length, resistance and the cross sectional area and the resistance and the radius of the conductor.

Useful formula:
The resistivity of the conductor is given by$\rho = \dfrac{{RA}}{L}$
Where $\rho $ is the resistivity of the conductor material, $R$ is the resistance of the conductor against the flow of the current, $A$ is the cross sectional area of the conductor and $L$ is the length of the conductor.

Complete step by step solution:
The resistance is the opposition to the flow of the current by the particles in the conductor. If the resistance is more, then the conductor is considered as the poor conductor or else good conductor of electricity. Let us consider the formula of the resistivity which is given above,
$\rho = \dfrac{{RA}}{L}$
Rearranging the formula of the resistivity to obtain the resistance,
$R = \dfrac{{\rho L}}{A}$
From the above formula, the relation between the resistance and the length and the area are formed.
$R\alpha L$ , $R\alpha \dfrac{1}{{\pi {r^2}}}$ and $R\alpha \dfrac{1}{A}$
Hence from the obtained relations, it is clear that the length is directly proportional to the resistance. And if the length increases the resistance of the conductor also increases. But the radius and the area are inversely proportional to the resistance.

Thus the option (A) is correct.

Note:The conductors that allow greater resistance are termed as poor conductors. The example of this type of conductor is Bismuth. On the other hand, if it offers low resistance to the current flow, then it is a good conductor. The example for this is iron, copper etc.