Two wires of equal diameters, of resistivities ρ 1 and ρ 2 and length l 1 and l 2 , respectively are joined in series. The equivalent resistivity of the combination is

Question

Two wires of equal diameters, of resistivities ρ 1 and ρ 2 and length l 1 and l 2 , respectively are joined in series. The equivalent resistivity of the combination is, ρ 1 l 1 + ρ 2 l 2 l 1 + l 2, ρ 1 l 2 + ρ 2 l 1 l 1 - l 2, ρ 1 l 2 + ρ 2 l 1 l 1 + l 2, ρ 1 l 1 + ρ 2 l 2 l 1 - l 2

MARKS App · Accepted Answer

Wires having frame diameter, hence area of cross-section will be equal, i.e. A 1 = A 2 = A R 1 = ρ 1 . l 1 A and R 2 = ρ 2 . l 2 A Since, both resistance are joined in series. Hence, R e q = R 1 + R 2 = ρ 1 . l 1 A + ρ 2 . l 2 A R e q = 1 A ρ 1 l 1 + ρ 2 l 2 ρ e q . l 1 + l 2 A = 1 A ρ 1 l 1 + ρ 2 l 2 ⇒ ρ e q = ρ 1 l 1 + ρ 2 l 2 l 1 + l 2

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