A cylindrical conductor of length L and uniform area of crosssection a has resistance R. Another conductor of length 2L and resistance R of the same material has an area of cross-section (a) A/2 (b) 3A/2 (c) 2A (d) 3A

Answer: (c) 2A

We know that the resistance of a wire of length (L) and having area of cross-section (A) is given by

R = ρ(L/A) where ρ is the resistivity constant of the conductor

It’s seen that,

The length is directly proportional to the resistance and the area of cross-section is inversely proportional to the resistance

So, when the length is doubled i.e., 2L and so the resistance will be 2R

Thus, for the resistance to remain the same as R, the area of cross-section should also be doubled as 2A

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