Question

Consider the insulating sheets with thermal resistance $R_1$ and $R_2$ as shown. The temperature at the ends of the arrangement is ${\theta }_1$ and ${\theta }_2$ then represent $\theta$ in term of given variables:

• A. $\frac{{\theta }_1{\theta }_2{R}_1{R}_2}{\left({\theta }_1{+\theta }_2\right)(R_1+R_2)}$
• B. $\frac{{\theta }_1{R}_1{+{\theta }_{2}R}_2}{(R_1+R_2)}$
• C. $\frac{\left({\theta }_1{+\theta }_2\right)R_1{R}_2}{R_1^2+R_2^2}$
• D. $\frac{{\theta }_1{R}_2+{\theta }_2{R}_1}{R_1+R_2}$

Answer 1

The correct option is D $\frac{{\theta }_1{R}_2+{\theta }_2{R}_1}{R_1+R_2}$

Heat current reaching the junction = heat current leaving the junction.

$\frac{{\theta }_1-\theta }{R_1}=\frac{\theta -{\theta }_2}{R_2}\Rightarrow \frac{{\theta }_1}{R_1}+\frac{{\theta }_2}{R_2}=\theta (\frac{1}{R_1}+\frac{1}{R_2})\Rightarrow \frac{{\theta }_1{R}_2+{\theta }_2{R}_1}{R_1{R}_2}=\theta \left(\frac{R_1+R_2}{R_1{R}_2}\right)\Rightarrow \theta =\frac{{\theta }_1{R}_2+{\theta }_2{R}_1}{R_1+R_2}$