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Question:

Two metal wires of identical dimension are connected in series. If σ₁ and σ₂ are the conductivities of the metal wires respectively, the effective conductivity of the combination is:

σ₁σ₂/(σ₁+σ₂)

(σ₁+σ₂)/(2σ₁σ₂)

(σ₁+σ₂)/σ₁σ₂

2σ₁σ₂/(σ₁+σ₂)

Solution:

here, Reff = R₁ + R₂
or (L + L) / σeffA = L / σ₁A + L / σ₂A (both wires are identical so have same cross section A)
or 2 / σeff = 1 / σ₁ + 1 / σ₂
or σeff = 2σ₁σ₂ / (σ₁ + σ₂)