Two rods A and B of different materials are welded together as shown in Fig. If their thermal conductivities are k1 and k2, the thermal conductivity of the composite rod will be

If the ends of the rods are maintained at temperatures θ1 and θ2 the rate of flow of heat through each rod is given by               Q1=k1Aθ1−θ2dQ2=k2Aθ1−θ2dwhere A is the cross-sectional area of each rod and d is the length of each rod. Now the cross-sectional area of the composite rod is 2A. If k is the thermal conductivity of the composite rod, the rate of heat flow is       Q=k(2A)θ1−θ2dBut Q=Q1+Q2. Therefore k(2A)θ1−θ2d=k1Aθ1−θ2d+k2Aθ1−θ2dor   k=12k1+k2Hence the correct choice is (d).