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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:

1. σ₁ + σ₂ / 2σ₁σ₂
2. σ₁σ₂
3. σ₁σ₂ / σ₁ + σ₂
4. 2σ₁σ₂ / σ₁ + σ₂

Correct answer: 2σ₁σ₂ / σ₁ + σ₂

Solution

When two wires are connected in series, the effective conductivity is determined by the harmonic mean of their individual conductivities. The formula for the effective conductivity is given by 2σ₁σ₂ / (σ₁ + σ₂).

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