Three conducting rods of same material and cross-section are shown in figure. Temperatures of A,D and C are maintained at 20^(@)C, 90^(@)C and 0^(@)C

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Three conducting rods of same material and cross-section are shown in figure. Temperatures of A,D and C are maintained at 20^(@)C, 90^(@)C and 0^(@)C. The ratio of lengths BD and BC if there is no heat flow in AB is

A. 2/7
B. 7/2
C. 9/2
D. 2/9

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There will be no heat flow through AB, if temperature of B is also 20^(@)C and heat current ini DB is equal to heat current in BC.

therefore H_(DB) = H_(BC)
or (70)/(I_(BD)//KA) = 20/(I_(BC)//KA) or (I_(BD)/I_(BC)) = 7/2`