Three rods of same dimensions are arranged as shown in the figure. They have thermal conductivities K₁ ,K₂ and K₃ . The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ and PQ. Which of the following options is correct?

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$K_{3} = \frac{1}{2} (K_{1} + K_{2})$

$K_{3} = K_{1} + K_{2}$

$K_{3} = \frac{K_{1} K_{2}}{K_{1} + K_{2}}$

$K_{3} = 2 (K_{1} + K_{2})$

answer is C.

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Detailed Solution

$Given {(\frac{Q}{t})}_{P R Q} = {(\frac{Q}{t})}_{PQ}$
$\frac{K_{s} A (Δθ)}{2 l} = \frac{K_{3} A (Δθ)}{l}, here K_{s} = \frac{2 K_{1} K_{2}}{K_{1} + K_{2}}$

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