A metallic wire having length *l* and area of cross-section A has a re

A metallic wire having length *l* and area of cross-section A has a resistance R. It is now connected in series with a wire of same metal but with length 2*l* and area of cross-section 2A. The total resistance of the combination will be:

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R/2

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UPSC Geoscientist – 2020

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The resistance of a metallic wire is given by the formula R = ρ * (l / A), where ρ is the resistivity of the material, l is the length, and A is the area of the cross-section. The first wire has resistance R = ρ * (l / A). The second wire is made of the same metal (same ρ), has length 2l, and area of cross-section 2A. Its resistance R₂ = ρ * (2l / 2A) = ρ * (l / A). Therefore, R₂ = R. When the two wires are connected in series, the total resistance is the sum of individual resistances: R_total = R₁ + R₂ = R + R = 2R.

The resistance of a wire is directly proportional to its length and inversely proportional to its area of cross-section. Resistances in series add up directly.

The resistivity (ρ) is a material property and remains constant for the same metal at the same temperature. In this case, both wires are made of the same metal, so their resistivity is the same.

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