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

`H_(1)=(K_(1)ADeltaT)/(l_(0))or,T_(PR)=(H_(1)l)/(K_(1)A)`
but `T_(PQ)=(H_(2)l)/(K_(3)A),T_(QR)=(H_(2)l)/(K_(3)'A)`
`T_(PR)=T_(PQ)+T_(QR)=(H_(2)l)/(A)((1)/(K_(2))+(1)/(K_(3)))or,(H_(1)l)/(K_(1)A)=(H_(2)l)/(A)((1)/(K_(2))+(1)/(K_(3)))"for " H_(1)=H_(2)`we have
`K_(3)=(K_(1)K_(2))/(K_(1)+K_(2))`