question_answer

Three identical rods A, B and C are placed end to end. A temperature difference is maintained between the free ends of A and C. The thermal conductivity of B is THRICE that of C and HALF that of A. The effective thermal conductivity of the system will be: (\[{{K}_{A}}\] is the thermal conductivity of rod A).

A) \[1/3{{K}_{A}}\]     

B)       \[3\,{{K}_{A}}\]    

C) \[2\,{{K}_{A}}\]                  

D)        \[2/3\,{{K}_{A}}\]

Correct Answer: A

Solution :

[a] \[{{R}_{A}}=\frac{\ell }{{{K}_{A}}A},\,\,{{R}_{B}}=\frac{\ell }{\frac{{{K}_{A}}}{2}\times A},\,{{R}_{C}}=\frac{\ell }{\frac{{{K}_{A}}}{6}\times A}\] \[{{R}_{A}}=\frac{3\ell }{kA}={{R}_{A}}+{{R}_{B}}+{{R}_{C}}\] \[=\frac{9\ell }{{{K}_{A}}\times A}\Rightarrow K=\frac{{{K}_{A}}}{3}\]