Two identical conducting rods AB and CD are connected to a circular conducting ring at two diametrically opposite points B and C, the radius of the ring is equal to the length of rods AB and CD. The area of cross-section, thermal conductivity of the rod and ring are equal. points A and D are maintained at temperatures of `100^(@)C` and `0^(@)C`. temperature at poimt C will be

Options

A. `62^(@)C`
B. `37^(@)C`
C. `28^(@)C`
D. `45^(@)C`

Answer

C

Explanation

For thermal resistance we use
`R_(AB) =(1)/(KA) =R_(CD)` `rArr``(R_(eq))_(BC) =(pi l)/(2KA)`
We have, `(100 - 0)/((2l)/(KA)+(pi l)/(2KA)) =(T_(c)-0)/((l)/(KA))`,
`rArr``T_(c) = 28^(@)`