Question

If the length and area of cross-section of a conductor are doubled, then its resistance will be:
(A) unchanged
(B) halved
(C) doubled
(D) quadrupled

Answer 1

The solution of this problem is determined by using the relation between the resistance of the conductor, resistivity of the conductor, length of the conductor, and the cross-section area of the conductor. This relation is given by the formula of the Resistivity of the conductor.

Formula used:
The resistivity of the conductor is given by,
$R = \dfrac{{\rho L}}{A}$
Where, $R$ is the resistance of the conductor, $\rho$ is the resistivity of the conductor, $L$ is the length of the conductor and $A$ is the cross-sectional area of the conductor.

Complete step by step answer:
Given that,
The length of the conductor is doubled, $L = 2L$
The area of cross section of a conductor is doubled, $A = 2A$
The resistivity of the conductor is given by,
$R = \dfrac{{\rho L}}{A}\,...............\left( 1 \right)$
By substituting the given length of the conductor and the area of cross section of the conductor in the equation (1), then the equation (1) is written as,
$\Rightarrow R = \dfrac{{\rho \left( {2L} \right)}}{{2A}}$
By rearranging the terms in the above equation, then the above equation is written as,
$\Rightarrow R = \dfrac{{2\rho L}}{{2A}}$
By cancelling the same terms, then the above equation is written as,
$\Rightarrow R = \dfrac{{\rho L}}{A} \Rightarrow R$
Thus, the above equation shows that the length of the conductor and the cross-section of the conductor are doubled, then the resistance of the conductor will remain the same, there is no change in the resistance of the conductor.

Hence, the option (A) is the correct answer.

Note:
By the equation (1), the resistance is directly proportional to the resistivity of the material and the length of the conducting material, and inversely proportional to the cross-sectional area of the conducting material. If the length of the conducting material is changed the resistance also changes. But here both area and length are changed, so there is no change in resistance.