Question

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 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. $1:8$

Answer 1

The correct option is D $1:8$

The rate of heat conduction is given by the formula

$\frac{dQ}{dt}=\frac{kA}{l}\Delta T$

Since $\Delta T$ is same in both the cases, the ratio is ,

$R=\frac{A_1}{A_2}\frac{l_2}{l_1}$

$R=\frac{d_1^2}{d_2^2}\frac{l_2}{l_1}=\frac{1}{4}\times \frac{1}{2}=\frac{1}{8}$