have thermal conductivities \[{{k}_{1}},\text{ }{{k}_{2}},\text{ }{{k}_{3}},\text{ }{{k}_{4}}\]and \[{{k}_{5}}\]when points A and B are maintained at different temperatures. No heat flows through the central rod if:
A) \[{{k}_{1}}{{k}_{4}}={{k}_{2}}{{k}_{3}}\]
B) \[{{k}_{1}}={{k}_{4}}\,and\,{{k}_{2}}={{k}_{3}}\]
C) \[\frac{{{k}_{1}}}{{{k}_{4}}}=\frac{{{k}_{2}}}{{{k}_{3}}}\]
D) \[{{k}_{1}}{{k}_{2}}={{k}_{3}}{{k}_{4}}\]
Correct Answer: A
Solution :
No heat will flow through CD if \[\frac{{{k}_{1}}}{{{k}_{2}}}=\frac{{{k}_{3}}}{{{k}_{4}}}\] \[{{k}_{1}}{{k}_{4}}={{k}_{2}}{{k}_{3}}\]
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