The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances $R _{1}$ and $R _{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by
JEE MAIN 2021, Medium
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Heat flow rate will be same through both
$\therefore \frac{\theta_{1}-\theta}{ R _{1}}=\frac{\theta-\theta_{2}}{ R _{2}}$
$R _{2} \theta_{1}- R _{2} \theta= R _{1} \theta- R _{1} \theta_{2}$
$\theta=\frac{ R _{2} \theta_{1}+ R _{1} \theta_{2}}{ R _{1}+ R _{2}}$
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