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

`Given((Q)/(t))_(PQR)=((Q)/(t))_(PQ)`
`(K_(s)A(Deltatheta))/(2l)=(K_(3)A(Deltatheta))/(t)hereK_(s)=(2K_(1)K_(2))/(K_(1)+K_(2))`
.