question_answer

Six identical conducting rods are joined as shown in figure. Points A and D are maintained at temperatures \[200{}^\circ C\] and \[20{}^\circ \text{ }C\] respectively. The temperature of junction B will be -

A) \[120{}^\circ C\]

B)                    \[100{}^\circ C\]

C)                    \[140{}^\circ C\]

D)                    \[\text{ }80{}^\circ C\]

Correct Answer: C

Solution :

\[{{H}_{1}}\,\,=\,\,2{{H}_{2}}\] \[\frac{KA}{\ell }\,\,(200-T)\,\,=\,\,2\frac{KA}{\ell }\,\left( T-T' \right)\] \[200=2T-T'\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......(1)\] \[2{{H}_{2}}={{H}_{3}}\] \[2\frac{KA}{\ell }\,\,(T-T')\,\,=\,\,\left( T'-20 \right)\,\frac{KA}{\ell }\] \[2T'-T=20\]         ?? (2) By solving (1) & (2) \[T\,\,=\,\,140\]