Two conductors have the same resistances at 0°C but their temperature coefficients of resistance are α₁ and α₂. The respective temperature coefficients for their series and parallel combinations are:
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Question

Two conductors have the same resistances at 0°C but their temperature coefficients of resistance are α₁ and α₂. The respective temperature coefficients for their series and parallel combinations are:

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G1 Physics · Accepted Answer

For equal initial resistances R: Series combination: Rₛ = R(1 + α₁ΔT) + R(1 + α₂ΔT) Hence, αₛ = (α₁ + α₂)/2 For parallel combination, neglecting higher-order small terms gives: αₚ = (α₁ + α₂)/2 Thus both are (α₁ + α₂)/2.