Solve this


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 :

  1. $\frac{\theta_{1} R_{2}+\theta_{2} R_{1}}{R_{1}+R_{2}}$

  2. $\frac{\theta_{1} R_{2}-\theta_{2} R_{1}}{R_{2}-R_{1}}$

  3. $\frac{\theta_{2} R_{2}-\theta_{1} R_{1}}{R_{2}-R_{1}}$

  4. $\frac{\theta_{1} R_{1}+\theta_{2} R_{2}}{R_{1}+R_{2}}$

Correct Option: 1



Temperature at the junction is $\theta$.

so using the formula




$\mathrm{R}_{1} \theta_{2}-\mathrm{R}_{1} \theta=\mathrm{R}_{2} \theta-\mathrm{R}_{2} \theta_{1}$

$\mathrm{R}_{1} \theta+\mathrm{R}_{2} \theta=\mathrm{R}_{1} \theta_{2}+\mathrm{R}_{2} \theta_{1}$

$\theta=\frac{R_{1} \theta_{2}+R_{2} \theta_{1}}{R_{1}+R_{2}}$

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