A wall consists of alternating blocks with length 'd' and coefficient of thermal conductivity $k_{1}$ and $k_{2} .$ The cross-sectional area of the blocks is the same. The equivalent coefficient of thermal conductivity of the wall between left and right is :

K_{1} + K_{2}

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\frac{(K_{1} + K_{2})}{2}

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\frac{K_{1} K_{2}}{K_{1} + K_{2}}

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\frac{2 K_{1} K_{2}}{K_{1} + K_{2}}

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Solution

The correct option is C $\frac{K_{1} K_{2}}{K_{1} + K_{2}}$
As per the given figure we observe that the conducting material are connected in parallel. Thus the equivalent coefficient of thermal conductivity will be given as $\frac{1}{k_{e q}} = \frac{1}{k_{1}} + \frac{1}{k_{2}}$
$\frac{1}{k_{e q}} = \frac{k_{2} + k_{1}}{k_{2} k_{1}}$
$k_{e q} = \frac{k_{2} k_{1}}{k_{2} + k_{1}}$

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