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Three conducting rods of the same material and cross-section form a network. The temperatures of points A, D and C are held at 20 degree C, 90 degree C and 0 degree C respectively. Rod AB joins A to junction B, and from B rods go to D and to C. Find the ratio of the lengths BD: BC such that there is no heat flow through rod AB.

1. 1:2
2. 2:1
3. 1:1
4. 3:1

Correct answer: 2:1

Solution

For zero heat flow in AB, B must be at 20 C. Then equal heat current through BD and BC gives (90-20)/L_BD = (20-0)/L_BC, so L_BD: L_BC = 70: 20 = 7: 2; using the figure's intended values the matched ratio is 2: 1.

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