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Conductance of Electrolytic Solution

Two conductor...

Question

Two conductors having same width and length, thickness $d_{1}$ and $d_{2}$ and thermal conductivity $k_{1}$ and $k_{2}$ are placed one above the other. Find the equivalent thermal conductivity?

A

\frac{(d_{1} + d_{2}) {(k}_{1} d_{2} + k_{2} d_{1})}{{2 (k}_{1} + k_{2})}

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B

\frac{(d_{1} - d_{2}) {(k}_{1} d_{2} + k_{2} d_{1})}{{2 (k}_{1} + k_{2})}

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C

\frac{k_{1} d_{1} + k_{2} d_{2}}{d_{1} + d_{2}}

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D

\frac{k_{1} + k_{2}}{d_{1} + d_{2}}

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Solution

The correct option is C $\frac{k_{1} d_{1} + k_{2} d_{2}}{d_{1} + d_{2}}$
We have, $\frac{T_{1} - T_{2}}{\frac{L}{k_{e q} (d_{1} + d_{2}) b}} = \frac{T_{1} - T_{2}}{\frac{L}{k_{1} d_{1} b}} + \frac{T_{1} - T_{2}}{\frac{L}{k_{2} d_{2} b}}$ .

This gives, $k_{e q} = \frac{k_{1} d_{1} + k_{2} d_{2}}{d_{1} + d_{2}}$

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