MCQ
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
  • A
    $\frac{\theta_{1} R_{1}+\theta_{2} R_{2}}{R_{1}+R_{2}}$
  • B
    $\frac{\theta_{1} R _{2}-\theta_{2} R _{1}}{ R _{2}- R _{1}}$
  • $\frac{\theta_{1} R _{2}+\theta_{2} R _{1}}{ R _{1}+ R _{2}}$
  • D
    $\frac{\theta_{1} R_{1}+\theta_{2} R_{2}}{R_{1}+R_{2}}$

Answer

Correct option: C.
$\frac{\theta_{1} R _{2}+\theta_{2} R _{1}}{ R _{1}+ R _{2}}$
c
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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