Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are K₁ and K₂. The thermal conductivity of the composite rod will be :  

\(\frac{K_1 + K_2}{2}\)

R = \(\frac{l}{KA}\)

\(\frac{1}{R}\) = \(\frac{1}{R_1}\) + \(\frac{1}{R_2}\)

\(\frac{1}{\frac{l}{K_{eff}A}}\) = \(\frac{1}{\frac{l}{K_1A/2}}\) + \(\frac{1}{\frac{l}{K_2A/2}}\)

On solving ,

K = \(\frac{K_1 +K_2}{2}\)