Three identical rods \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C}...

Three identical rods \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) 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 \( \left(\mathrm{K}_{\mathrm{A}}\right. \) is the thermal conductivity of \( \left.\operatorname{rod} \mathrm{A}\right) \)
a. \( \frac{1}{3} \mathrm{~K}_{\mathrm{A}} \)
b. \( 3 \mathrm{~K}_{\mathrm{A}} \)
c. \( 2 \mathrm{~K}_{\mathrm{A}} \)
d. \( \frac{2}{3} \mathrm{~K}_{\mathrm{A}} \)