Question

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 of that of A The effective thermal conductivity of the system will be
$(k_A$ is the therm al conductivity of rod A)

• A. $\frac{1}{3}{K}_A$
• B. $3K_A$
• C. $2K_A$
• D. $\frac{2}{3}{K}_A$

Answer 1

Answer: (A)

Given, $K_B=K_A/2,$
and $K_B=3K_C$
$\therefore K_C=K_A/6$
Rods are in series form so
$\frac{L}{K}=\frac{l_1}{K_A}+\frac{l_2}{K_B}+\frac{l_3}{K_C}$
$\left(\because l=l_1=l_2=l_3\right)$
$\frac{3l}{K}=\frac{l}{K_A}+\frac{l}{K_A/2}+\frac{l}{K_A/6}$
or $\frac{3l}{K}=\frac{9l}{K_A}$
or $K=\frac{K_A}{3}$