Q.

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 1000C and 00C. Temperature at point C will be

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a

620C

b

370C

c

280C

d

450C

answer is C.

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Detailed Solution

RAB=RCD=R( say )Length of semi-circle =πl∴   Resistance of semi-circle  =πR (∵R∝l)      RBC=πR2 (in parallel)    Heat current,   H=100−0R+R+π2⋅R=28R units Now,   θC−00=HR=28RR∴ θC=280C
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