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

Both rods are connected in parallel
` (Delta Q)/(d) = (Delta Q_1)/(d) + (Delta Q_2)/(d)`
` = (K_1a (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) ]`