Two rods of same area of cross-section and lengths and conductivities K₁ and K₂ are connected in series. Then in steady state, conductivity of the combination is

Step-by-step solution

The thermal resistance of a rod is given by R= l K A As, length and area of two rods are same, then in series combination, aligned R &=R₁+R₂ & 2 l K_ s A &= l K₁ A + l K₂ A & 2 K_ s &= 1 K₁ + 1 K₂ = K₁+K₂ K₁ K₂ & K_ s &= 2 K₁ K₂ K₁+K₂ aligned