Question

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 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 double that of across BC
• D. Potential difference across AB is 4 times that of across BC

Answer 1

Answer: (A)

Current flowing through both the bars is equal.
Now, the heat produced is given by
$H = I^2 Rt \, or H \propto R \, or \frac{H_{AB}}{H_{BC}}= \frac{R_{AB}}{R_{BC}}$
$= \frac{(1/2r)^2}{(1/r)^2} \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \big( as \, R \propto \frac{1}{A} \propto \frac{1}{r^2}\big)$
$= \frac{1}{4} \, or \, H_{BC} = 4H_{AB}$