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

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If the ends of the rods are maintained at temperatures θ$$1$$ and θ$$2$$ the rate of flow of heat through each rod is given by               $$Q1=k1A$$θ$$1$$−θ$$2dQ2=k2A$$θ$$1$$−θ$$2dwhere$$ 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       $$Q=k(2A)$$θ$$1$$−θ$$2dBut$$ $$Q=Q1+Q2$$. Therefore $$k(2A)$$θ$$1$$−θ$$2d=k1A$$θ$$1$$−θ$$2d+k2A$$θ$$1$$−θ$$2dor$$   $$k=12k1+k2Hence$$ the correct choice is (d).

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