If the length of a wire is doubled and the cross-sectional area remains the same, what happens to its resistan

Question

If the length of a wire is doubled and the cross-sectional area remains the same, what happens to its resistance?

Examoogle · Accepted Answer

The correct answer is Option B: It becomes double. The resistance of a conductor is directly proportional to its length. When the length is doubled while the cross-sectional area remains constant, the resistance also doubles.

Step-by-Step Solution & Concepts:
The resistance of a conductor is directly proportional to its length. When the length is doubled while the cross-sectional area remains constant, the resistance also doubles.

Working Principle: Resistance ($R$) is governed by the formula $R = \rho \frac{l}{A}$, where $\rho$ is resistivity, $l$ is length, and $A$ is the cross-sectional area. Since $R \propto l$, doubling $l$ while keeping $\rho$ and $A$ constant results in a proportional doubling of the total resistance.

Key Formulas: $R = \rho \frac{l}{A}$ — Resistance formula where $\rho$ is resistivity, $l$ is length, and $A$ is area.; $R \propto l$ — Resistance is directly proportional to length.

Key Points: Resistance increases linearly with length if the material and thickness are unchanged.; Resistivity ($\rho$) is an intrinsic property of the material and does not change with physical dimensions.; If the area were increased instead of length, resistance would decrease proportionally.

Applications: Electrical wiring in buildings; Design of heating elements and resistors

Additional Info: The constant of proportionality $\rho$ (resistivity) depends only on the material type and temperature.. Option D is incorrect because resistance becomes four times only if both length is doubled and area is halved, or if length is doubled and the wire is stretched (which reduces area).

Answer: B is correct — Resistance is directly proportional to the length of the conductor, so doubling the length doubles the resistance.

Exam Tip: Always check if the problem specifies 'stretching' the wire versus 'adding' a wire. Stretching changes both length and area simultaneously, whereas 'doubling length' implies adding segments or assuming $A$ is constant.

Examoogle · Answer

Option A: It remains the same

Examoogle · Answer

Option C: It becomes half

Examoogle · Answer

Option D: It becomes four times

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)