The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances $\mathrm{R}_{1}$ and $\mathrm{R}_{2}$ as well as top and bottom temperatures $\theta_{1}$ and $\theta_{2}$ (as shown in figure) is given by :
Correct Option: 1
(1)
Temperature at the junction is $\theta$.
so using the formula
$\frac{T_{2}-T}{R_{1}}=\frac{T-T_{1}}{R_{2}}$
$\frac{\theta_{2}-\theta}{\mathrm{R}_{2}}=\frac{\theta-\theta_{1}}{\mathrm{R}_{1}}$
$\mathrm{R}_{1}\left(\theta_{2}-\theta\right)=\mathrm{R}_{2}\left(\theta-\theta_{1}\right)$
$\mathrm{R}_{1} \theta_{2}-\mathrm{R}_{1} \theta=\mathrm{R}_{2} \theta-\mathrm{R}_{2} \theta_{1}$
$\mathrm{R}_{1} \theta+\mathrm{R}_{2} \theta=\mathrm{R}_{1} \theta_{2}+\mathrm{R}_{2} \theta_{1}$
$\theta=\frac{R_{1} \theta_{2}+R_{2} \theta_{1}}{R_{1}+R_{2}}$