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

Answer

B

Explanation

`overset(**)(Q) = (T_(A) - T_(B))/((L)/(k_(3)A)) =(T_(A) - T_(B))/((L)/(k_(1)A) + (L)/(k_(2)A)) implies k_(3) = (k_(1)k_(2))/(k_(1) + k_(2))`