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Two identical metal wires of thermal conductivities K1 and K2 respectively are connected in series. The effective thermal conductivity of the combination is

1. 2K1K2/(K1 + K2)
2. (K1 + K2)/(2K1K2)
3. (K1 + K2)/(K1K2)
4. K1K2/(K1 + K2)

Correct answer: 2K1K2/(K1 + K2)

Solution

For two identical wires (same length and area) joined in series, equal heat current through both gives effective conductivity K_eff = 2K1K2/(K1 + K2) (harmonic-mean form).

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