Q.
Two bars of radius $r$ and $2r$ are kept in contact as shown. An electric current $i$ is passed through the bars. Which one of the following is correct?
A) Heat produced in bar $BC$ is 4 times the heat produced in bar $AB$
B) Electric field in both halves is equal
C) Current density across $AB$ is doubled that of across $BC$
D) Potential difference across $AB$ is 4 times that of across $BC$
Explanation
(a) Current flowing through both the bars is equal. Now, the heat produced is given by
$H = I^{2}Rt$
or $H \propto R\ or\ \frac{H_{AB}}{H_{Bc}} = \frac{R_{AB}}{R_{BC}}$
$= \frac{\left( \frac{1}{2r} \right)^{2}}{\left( \frac{1}{r} \right)^{2}}\ \ \left( \because R \propto \frac{1}{A} \propto \frac{1}{r^{2}} \right)$
$= \frac{1}{4}$
or $H_{BC} = 4H_{AB}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.