Q. Three rods of same dimensions are arranged as shown in figure. They have thermal conductivities $K_{1},K_{2}$ and $K_{3}$. The points $P$ and $Q$ are maintained at different temperatures for the heat to flow at the same rate along $PRQ$ and $PQ$ then which of the following options is correct
A) $K_{3} = \frac{1}{2}(K_{1} + K_{2})$
B) $K_{3} = K_{1} + K_{2}$
C) $K_{3} = \frac{K_{1}K_{2}}{K_{1} + K_{2}}$
D) $K_{3} = 2(K_{1} + K_{2})$
Explanation
(c) The given arrangement of rods can be redrawn as follows
It is given that $H_{1} = H_{2}$
$\Rightarrow \frac{KA(\theta_{1} - \theta_{2})}{2l} = \frac{K_{3}A(\theta_{1} - \theta_{2})}{l} \Rightarrow K_{3} = \frac{K}{2} = \frac{K_{1}K_{2}}{K_{1} + K_{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.