Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are `K_(1)` and `K_(2)`. The thermal conductivity of the composite rod will be

Options

A. `(K_(1) + K_(2))/(2)`
B. `(3(K_(1) + K_(2)))/(2)`
C. `K_(1) + K_(2)`
D. `2(K_(1) + K_(2))`

Answer

A

Explanation

Let K be the thermal conductivity of composite rod. Then rate of heat flowing through rod is
`H = H_(1) + H_(2)`
`(K A(T_(1) - T_(2)))/(d) = (K_(1)A(T_(1) - T_(2)))/(d) + (K_(2)A(T_(1) - T_(2)))/(d)`
or `2 K = K_(1) + K_(2)`
or `K =(K_(1) + K_(2))/(2)`