Three rods of same dimensions are arranged as shown in Fig. They have thermal conductivities `K_1`,`K_2` and `K_3`. The points P and Q are maintained at different temeperature for the heat to flow at the same rate along PRQ and PQ. Whi of the following options correct?

Options

A. `K_3=1/2(K_1+K_2)`
B. `K_3=K_1+K_2`
C. `K_3=(K_1K_2)/(K_1+K_2)`
D. `K_3=2(K_1+K_2)`

Answer

C

Explanation

H `rarr` heat current

Given, `H_1=H_2`
`implies (KA(T_1-T_2))/(2l)=(K_3A(T_1-T_2))/(l)`
`implies K_3=K/2=(K_1K_2)/(K_1+K_2)` [as `K=(2K_1K_2)/(K_1+K_2)`].