Two metal wires having the same length and same cross-sectional area are joined in series. If their conductivities are sigma1 and sigma2, what is the effective conductivity of the series combination?

sigma1 sigma2 / (sigma1 + sigma2)
2 sigma1 sigma2 / (sigma1 + sigma2)
(sigma1 + sigma2) / (2 sigma1 sigma2)
(sigma1 + sigma2) / (sigma1 sigma2)

Correct answer: 2 sigma1 sigma2 / (sigma1 + sigma2)

Solution

Adding the two equal-length resistances and equating to one wire of double length gives the harmonic-type result 2 sigma1 sigma2 / (sigma1 + sigma2).

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