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

Answer

D

Explanation

In parallel `(1)/(R_(eq)) = (1)/(R_1) +(1)/(R_2)`
`(K_(eq)(2A))/(l) = (k_(l)A)/(l)+(K_(2)A)/(l)`
`K_(eq) = (K_(1)+K_(2))/(2)`.