Three conducting rods of same material and cross-section are showm in Fig .7(CF).22. Temperatures of A, D and C are maintained at `20^(@)C, 90^(@)C` and `0^(@)C` . The ratio of the lengths of BC and BD, if there is no flow in AB, is

Options

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

Answer

C

Explanation

Since there is no flow of heat in rod AB, so temperature at B is equal to temperature at A, i.e.,
`theta_(B) =theta_(A) =20^(@)C`
Heat flowing through DB per sec, = heat flowing through BC per sec.

`(KA(90^(@) - 20^(@)))/(l_(BD)) = (KA(20^(@) - 0^(@)))/(l_(BD))`
`:. (l_(BD))/(l_(BD)) =(2)/(7)`