Two metallic wires of identical dimensions are connected is series. If σ 1 and σ 2 are the conductivities of the these wires respectively, the effective conductivity of the combination is :

Step-by-step solution

Let length of wire be l , Area of wire as A For equivalent wire length = 2 l & area will be A As the wires are connected in series combination, the thermal resistance R e q = R 1 + R 2 ⇒ 2 l σ eq   A = l σ 1   A + l σ 1   A ⇒ 2 σ eq   = 1 σ 1 + 1 σ 2 ⇒ σ eq   = 2 σ 1 σ 2 σ 1 + σ 2