Question

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

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

Answer 1

Correct Answer - C
`R_(AB) = R_(CD)=R`(say)
Length of semicircle = `pil`
Resistance of semicircle = `piR` as `Ralphal`
`R_(BC) = (piR)/2`(in parallel)
Heat current, H = `(100-0)/(R+R+(pi)/2.R)=28/R` units
Now, `theta_(C) - 0^(@)` = HR = `28^(@)`C
`theta_(C)` = `28^(@)`C