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

Thermal current
`H=H_(1)+H_(2)`
`=(K_(1)A(T_(1)-T_(2)))/(d)+(K_(2)A(T_(1)-T_(2)))/(d)`
`(K_(EQ)2A(T_(1)-T_(2)))/(d)=(A(T_(1)-T_(2)))/(d)[K_(1)+K_(2)]`
`K_(EQ)=[(K_(1)+K_(2))/(2)]`