How does the resistance of a metallic conductor change if its length is tripled while keeping the area of cros

Question

How does the resistance of a metallic conductor change if its length is tripled while keeping the area of cross-section constant?

Examoogle · Accepted Answer

The correct answer is Option C: It becomes three times. The resistance of a metallic conductor is directly proportional to its length. When the length of the conductor is tripled while keeping its cross-sectional area and material constant, its resistance increases proportionally by a factor of three.

Step-by-Step Solution & Concepts:
The resistance of a metallic conductor is directly proportional to its length. When the length of the conductor is tripled while keeping its cross-sectional area and material constant, its resistance increases proportionally by a factor of three.

Working Principle: According to the laws of electrical resistance, the resistance $R$ of a uniform conductor is given by the formula $R = \rho \frac{l}{A}$, where $\rho$ is the resistivity, $l$ is the length, and $A$ is the cross-sectional area. Since the material and area remain unchanged, tripling the length ($3l$) results in a direct tripling of the total resistance.

Key Formulas: $R = \rho \frac{l}{A}$ — Resistance formula in terms of length, area, and resistivity; $R \propto l$ — Direct proportionality between resistance and length for a constant cross-sectional area

Key Points: Resistance is directly proportional to the length of a conductor ($R \propto l$).; Resistance is inversely proportional to the cross-sectional area of a conductor ($R \propto \frac{1}{A}$).; Resistivity ($\rho$) depends only on the nature of the material and temperature, not on its physical dimensions.

Applications: Design of variable resistors and rheostats; Calculating voltage drops across long electrical transmission lines

Additional Info: Resistivity remains constant because the material properties and temperature do not change.. Option D is a common misconception where students incorrectly square the length factor, mistaking it for area changes.

Answer: C is correct — The resistance becomes three times the original value because resistance is directly proportional to the length of the conductor.

Exam Tip: Always read the question carefully to see if the conductor's volume is kept constant (stretched) or if just the length is modified while area remains constant, as stretching a wire simultaneously decreases its cross-sectional area!

Examoogle · Answer

Option A: It becomes one-third

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Option B: It remains the same

Examoogle · Answer

Option D: It becomes nine times

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