Three rods of same material, same area of cross-section but different lengths 10 cm, 20 cm and 30 cm are connected at a point as shown. What is temperature of junction O (in °C)?

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Ans (16.36)

Let junction temperature = T.

$\frac{T - 20}{R _{1}} + \frac{T - 30}{R _{2}} + \frac{T - 10}{R _{3}} = 0$ with $R \propto ℓ$ (same material, same area): $\frac{T - 20}{20} + \frac{T - 30}{30} + \frac{T - 10}{10} = 0$

$3 (T - 20) + 2 (T - 30) + 6 (T - 10) = 0 \Rightarrow 11 T = 180 \Rightarrow T = 16.3 6^{\circ}$ C

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