question_answer

Three rods of same dimensions are arranged as shown in figure they have thermal conductivities \[{{K}_{1}},{{K}_{2}}\] and\[{{K}_{3}}\] The points P and Q are maintained at different temperatures for the heat to flow at the same rate along PRQ  and PQ then which of the following option is correct                [KCET 2001]

A)            \[{{K}_{3}}=\frac{1}{2}({{K}_{1}}+{{K}_{2}})\]

B)            \[{{K}_{3}}={{K}_{1}}+{{K}_{2}}\]

C)            \[{{K}_{3}}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]

D)            \[{{K}_{3}}=2({{K}_{1}}+{{K}_{2}})\]

Correct Answer: C

Solution :

                   The given arrangement of rods can be redrawn as follows It is given that H1 = H2 Þ \[\frac{KA({{\theta }_{1}}-{{\theta }_{2}})}{2l}=\frac{{{K}_{3}}A({{\theta }_{1}}-{{\theta }_{2}})}{l}\]Þ \[{{K}_{3}}=\frac{K}{2}=\frac{{{K}_{1}}{{K}_{2}}}{{{K}_{1}}+{{K}_{2}}}\]