Q. 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 productivity of $B$ is thrice that if $C\ $and half of that of $A$. the effective thermal conductivity of the system will be ($KA$ is the thermal conductivity of rod $A$)
A) $\frac{3}{2}$ $KA$
B) 2 $KA$
C) $3\ KA$
D) $\frac{1}{3}\ KA$
Explanation
(d) [table] A | B | C [/table]
$K_{B} = \frac{K_{A}}{2}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{B} = 3K_{C}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{C} = \frac{K_{A}}{6}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{l}{K_{s}} = \frac{l_{1}}{K_{A}} + \frac{l_{2}}{K_{B}} + \frac{l_{3}}{K_{C}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3l}{K_{S}} = \frac{l}{K_{A}} + \frac{l}{\frac{K_{A}}{2}} + \frac{l}{\frac{K_{A}}{6}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{3l}{K_{S}} = \frac{9l}{K_{A}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{S} = \frac{K_{A}}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.