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_(1)K_(2))/(K_(1) + K_(2))`
D. `K_(3) = 2(K_(1) + K_(2))`

Answer

C

Explanation

`because R_(PR) = R_(RQ) =R_(PQ)`
`therefore 1/(K_(1)A) + 1/(K_(2)A)= 1/(K_(3)A) or K_(3) = (K_(1)K_(2))/(K_(1)+K_(2))`