Q. Wires $A$ and $B$ have identical lengths and have circular cross-section. The radius of $A$ is twice the radius of $B\ i.e.\ r_{A} = 2r_{B}$. For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is given by
A) $K_{A} = 4K_{B}$
B) $K_{A} = 2K_{B}$
C) $K_{A} = K_{B}/2$
D) $K_{A} = K_{B}/4$
Explanation
(d) $\frac{Q}{t} = \frac{KA\mathrm{\Delta}\theta}{l} \Rightarrow \frac{K_{A}}{K_{B}} = \frac{A_{B}}{A_{A}} = \left( \frac{r_{B}}{r_{A}} \right)^{2} = \frac{1}{4} \Rightarrow K_{A} = \frac{K_{B}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.