Which statement is true regarding the factors affecting the resistance of a conductor?

Question

Examoogle · Accepted Answer

The correct answer is Option C: Resistance is directly proportional to the resistivity of the material. The resistance of a conductor is directly proportional to its resistivity, which is an intrinsic property of the material. This means materials with higher resistivity offer greater opposition to the flow of electric current under identical geometric conditions.

Step-by-Step Solution & Concepts:
The resistance of a conductor is directly proportional to its resistivity, which is an intrinsic property of the material. This means materials with higher resistivity offer greater opposition to the flow of electric current under identical geometric conditions.

Working Principle: Resistance is defined by the formula $R = \rho \frac{l}{A}$. Here, $R$ is directly proportional to the material property resistivity ($\rho$), directly proportional to length ($l$), and inversely proportional to the area of cross-section ($A$). As electrons drift through a conductor, they collide with ions in the lattice; materials with higher resistivity increase the frequency or impact of these collisions, thereby increasing resistance.

Key Formulas: $R = \rho \frac{l}{A}$ — Where $R$ is resistance, $\rho$ is resistivity, $l$ is length, and $A$ is cross-sectional area.

Key Points: Resistivity ($\rho$) depends solely on the nature of the material and temperature.; Resistance increases with an increase in length because electrons undergo more collisions.; Resistance decreases with an increase in cross-sectional area as more paths are available for electron flow.

Applications: Selection of materials for heating elements (high resistivity).; Selection of materials for electrical wiring (low resistivity).

Additional Info: Resistivity is measured in Ohm-meters ($\Omega \cdot m$).. Option A is incorrect because $R \propto l$.. Option B is incorrect because $R \propto \frac{1}{A}$.. Option D is incorrect because $R$ typically increases with temperature for conductors.

Answer: C is correct — Resistance is directly proportional to the resistivity of the material.

Exam Tip: Always remember that resistance is a physical property of the device, whereas resistivity is an intrinsic property of the substance itself.

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Option A: Resistance is inversely proportional to the length of the conductor

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Option B: Resistance is directly proportional to the area of cross-section

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Option D: Resistance does not depend on temperature

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