Q. The same mass of copper is drawn into two wires $1\ mm$ and $2\ mm$ thick. Two wires are connected in series and current is passed through them. Heat produced in the wire is in the ratio
A) 2 :1
B) 1 :16
C) 4 :1
D) 16 :1
Explanation
(d) $H = i^{2}RT = i^{2}\left( \frac{\rho l}{A} \right)t = \frac{i^{2}\rho Vt}{A^{2}}\ \ \ \ \ \lbrack V = volume = Al\rbrack$
$\Rightarrow H \propto \frac{1}{r^{4}} \Rightarrow \frac{H_{1}}{H_{2}} = \left( \frac{r_{2}}{r_{1}} \right)^{4} = \left( \frac{2}{1} \right)^{4} = \frac{16}{1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.