If two metallic plates of equal thicknesses and thermal conductivities $K_1$ and $K_2$ are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be
$(a) \frac{K_1 K_2}{K_1 + K_2} \quad (b) \frac{2 K_1 K_2}{K_1 + K_2} \\ (c) \frac{(K_1^2 + K_2^2)^{3/2}}{K_1 K_2} \quad (d) \frac{(K_1^2 + K_2^2)^{3/2}}{2 K_1 K_2}$
Text Solution
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In series $R_{eq} = R_1 + R_2 \Rightarrow \frac{2l}{K_{eq} A} = \frac{1}{K_1 A} + \frac{1}{K_2 A}$ $\Rightarrow \frac{2}{K_{eq}} = \frac{1}{K_1} + \frac{1}{K_2} \Rightarrow K_{eq} = \frac{2 K_1 K_2}{K_1 + K_2}$
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