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The temperature $θ$ at the junction of two insulating sheets, having thermal resistances $R_{1}$ and $R_{2}$ as well as top and bottom temperatures $θ_{1}$ and $θ_{2}$ (as shown in figure) is given by:

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$\frac{θ_{1} R_{2} - θ_{2} R_{1}}{R_{2} - R_{1}}$

$\frac{θ_{2} R_{2} - θ_{1} R_{1}}{R_{2} - R_{1}}$

$\frac{θ_{1} R_{2} + θ_{2} R_{1}}{R_{1} + R_{2}}$

$\frac{θ_{1} R_{1} + θ_{2} R_{2}}{R_{1} + R_{2}}$

answer is C.

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Detailed Solution

$\begin{array}{l} At steady state, heat flow rate wil be same. \\ \Rightarrow \frac{θ_{1} - θ}{R_{1}} = \frac{θ - θ_{2}}{R_{2}} \\ \Rightarrow θ = \frac{θ_{1} R_{2} + θ_{2} R_{1}}{R_{1} + R_{2}} \end{array}$

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