Q. Two conductors of the same material have their diameters in the ratio 1 : 2 and their lengths in the ratio 2 : 1. If the temperature difference between their ends is the same, then the ratio of amounts of heat conducted per second through them will be
A) $4\ :1$
B) $1\ :4$
C) $8\ :1$
D) $1\ :8$
Explanation
(d) The residence of conductor
$R = \frac{\rho l}{A} = \frac{1}{\pi r^{2}}$
$or\ \ \ R \propto \frac{l}{r^{2}}$
$\therefore\ \frac{R_{1}}{R_{2}} = \frac{l_{1}}{l_{2}} \times \frac{r_{2}^{2}}{r_{1}^{2}} = \frac{2}{1} \times \left( \frac{2}{1} \right)^{2} = \frac{8}{1}$
Thermal potential between the ends of the roads are same. So, heat conducted per second
$H = \frac{\mathcal{Q}}{t} \propto \frac{1}{R}$
$\therefore\frac{H_{1}}{H_{2}} = \frac{R_{2}}{R_{1}} = \frac{1}{8} = 1:8$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.