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When the length and area of cross-section both are doubled, then its resistance

Question

When the length and area of cross-section both are doubled, then its resistance

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Solution

The resistance of a conductor is given by the formula:

R = ρL/A

where: R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the conductor, and A is the cross-sectional area of the conductor.

If both the length (L) and the cross-sectional area (A) are doubled, then the new resistance (R') is given by:

R' = ρ(2L)/(2A)

Simplifying this gives:

R' = ρL/A

This is the same as the original resistance (R). Therefore, when both the length and the cross-sectional area of a conductor are doubled, its resistance remains the same.

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