Six identical cunducting rods are joined as shown in Fig. Points A and D are maintained at temperatures `200^@C` and `20^@C` respectively. The temperature of junction B will be

Options

A. `120^(@)C`
B. `100^(@)C`
C. `140^(@)C`
D. `80^(@)C`

Answer

C

Explanation

Let thermal resistance of each rod is R
Effective thermal resistance between B and D = 2R
We use `T_(B) =(R_(1)T_(2)+R_(2)T_(1))/(R_(1)+R_(2))`
`rArr``T_(B) =(R(20)+2R(200))/(R+2R)`
`rArr` `T_(B) =(420 R)/(3 R) =140 ^(@)C`