Three rods of same dimensions are arranged as shown in the figure. They have thermal conductivities `K_(1)`, `K_(2)` and `K_(3)`. The points A and B are maintained at different temperatures. For the heat to flow at the same rate along ACB and AB,

Options

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

Answer

A

Explanation

For steady flow, conductivity along ACB = Along AB
`(K_(1)K_(2))/((K_(1) + K_(2))//l) = (K_(3))/(l) or (K_(1) K_(2))/(K_(1) + K_(2)) = K_(3)`