Question

The resistance of a conductor is inversely proportional to its:
(A) Area of cross- section
(B) Length
(C) Specific resistance
(D) Density

Answer 1

Identify the formula of the resistance that it must have the parameters given in the options. From that find the parameter that is directly proportional to the resistance and the parameter that is inversely proportional to its resistance.

Useful formula:
The formula of the resistance of the conductor is given by
$R = \dfrac{{\rho L}}{A}$
Where $R$ is the specific resistance of the conductor, $\rho$ is the density of the conductor, $L$ is its length and $A$ is the cross sectional area of the conductor.

Complete step by step solution:
The resistance is the opposition to the flow of the current. It varies with the type of the material. By using the formula of the resistance,
$R = \dfrac{{\rho L}}{A}$
By finding the parameters and its relation with that of the resistance.
$R\alpha \rho L$
From the above proportionality, it is clear that the resistance is directly proportional to the specific resistance and the length of the conductor. If the resistivity and the length increases, then the resistance also increases.
$R\alpha \dfrac{1}{A}$
But the resistance is inversely proportional to the cross sectional area of the conductor. If the conductor possesses a greater cross sectional area, then its resistance will be less.

Thus the option (A) is correct.

Note: The term mentioned in the formula, specific resistance is the resistance in the conductor per unit length and per unit cross sectional area. It is also specified by the term resistivity. If the material of the conductor has the low resistivity, then it readily allows the electric current to pass through.