Three rods of same dimensions have thermal conductivities 3K, 2K and K. They are arranged as shown in the figure below.

If the temperature of the junction in steady state is $\frac{200^{0} C}{x}$ , then x is ________.

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answer is 3.

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Detailed Solution

According to Kirchoff 1st law $i = i_{1} + i_{2}$
Then the temperature of the junction in steady state is
$(100 - T) 3 k = (T - 50) 2 k + (T - 0) k \Rightarrow T = \frac{200}{3}^{0} C$

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