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 :
Show Hint
- \(\frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}\)
- \(\frac{\theta_1 R_1 + \theta_2 R_2}{R_1 + R_2}\)
- \(\frac{\theta_1 R_2 - \theta_2 R_1}{R_2 - R_1}\)
- \(\frac{\theta_2 R_2 - \theta_1 R_1}{R_2 - R_1}\)
The Correct Option is A
Solution and Explanation
The sheet of resistance \(R_1\) lies between \(\theta_1\) and \(\theta\), and the sheet of resistance \(R_2\) lies between \(\theta\) and \(\theta_2\).
\(\frac{\theta_1-\theta}{R_1} = \frac{\theta-\theta_2}{R_2}\)
\(\theta_1 R_2 - \theta R_2 = \theta R_1 - \theta_2 R_1\)
\(\theta (R_1 + R_2) = \theta_1 R_2 + \theta_2 R_1\)
\(\theta = \frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}\)
Answer: (1) \(\frac{\theta_1 R_2 + \theta_2 R_1}{R_1 + R_2}\)
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