Consider two insulating sheets with thermal resistances R_1 and R… - Vidyadip

MCQ

Consider two insulating sheets with thermal resistances $R_1$ and $R_2$ as shown. The temperatures $\theta $ is

A
$\frac{{{\theta _1}{\theta _2}{R_1}{R_2}}}{{({R_1} + {R_2})({\theta _1} + {\theta _2})}}$
B
$\frac{{{\theta _1}{R_1} + {\theta _2}{R_2}}}{{{R_1} + {R_2}}}$
C
$\frac{{({\theta _1} + {\theta _2})\left( {{R_1}{R_2}} \right)}}{{R_1^2 + R_2^2}}$
✓
$\frac{{{\theta _1}{R_2} + {\theta _2}{R_1}}}{{{R_1} + {R_2}}}$

✓

Answer

Correct option: D.

$\frac{{{\theta _1}{R_2} + {\theta _2}{R_1}}}{{{R_1} + {R_2}}}$

d
Heat flow in $(1)=$ Heat flow in $(2)$

$\frac{\Delta \mathrm{T}_{1}}{\mathrm{R}_{1}}=\frac{\Delta \mathrm{T}_{2}}{\mathrm{R}_{2}}$

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

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