Four rods of material `X` and three rods of material `Y` are connected as shown in figure. All the rods are of identical lengths and cross-sectional area. Given thermal resistance of rod of material `X, R_(x) = R` and thermal conductivities of materials are related by relation `K_(Y) = 2K_(X)`.

`{:(,"Column-I",,"Column-II"),((A),"Thermal resistance between B and E" ,(p),(500)/(13).^(@)C ),((B),"Thermal resistance between A and F" ,(q),(700)/(13).^(@)C ),((C),"Temperature of junction B" ,(r),(2R)/(3)), ((D),"Temperature of junction D" ,(s),(13R)/(6)):}`

Explanation

For (A)
`R_(Y) = (l)/(K_(Y)A) = (l)/(2K_(X)A) = (R)/(2)`
No heat current flows through rod `CD`


For(B)

For (C)
Total heat current form `A` to `F`,
`I = (100-0)/((13)/(6)R) = (600)/(13R)`
Let temperature of `B` be `T_(B)` then `l=(100-T_(B))/(R) = (600)/(13R) implies T_(B) = (700)/(13) "^(@)C`
For (D) As current in inversely proportional to heat resistance.
So heat current in `BD`
= `((2R)/(R +2R))I = (2)/(3)I`
`implies (T_(B) - T_(D))/(R//2) = (2)/(3)I = (2)/(3)((600)/(13R))`
`implies T_(D) = (700)/(13) - (200)/(13) = (500)/(13) "^(@)C`