question_answer

Three conducting rods of same material and cross-section are shown in figure. Temperatures of A, D and C are maintained at \[20{}^\circ C,\text{ }90{}^\circ C\] and \[0{}^\circ C\]. The ratio of lengths of BD and BC if there is no heat flow in AB is:

A) 2/7

B) 7/2

C) 9/2

D) 2/9

Correct Answer: B

Solution :

[b] There is no heat flow through AB. Hence \[{{\theta }_{B}}={{20}^{o}}C\,{{H}_{DB}}={{H}_{BC}}\]

\[\therefore \]      \[\frac{(90-20)}{{{l}_{BD}}/KA}=\frac{(20-0)}{{{l}_{BC}}/KA}\]

\[\therefore \]      \[\frac{{{l}_{BD}}}{{{l}_{BC}}}=\frac{7}{2}\]