Q. When a current is passed in a conductor, 3$℃$ rise in temperature is observed. If the strength of current is increased by two times, then rise in temperature will approximately be
A) 36$℃$
B) 27$℃$
C) 18$℃$
D) 9$℃$
Explanation
(b) $H = I^{2}Rt = mc\mathrm{\Delta}\theta$
$\therefore\mathrm{\Delta}\theta \propto I^{2}$
Hence$\ \frac{\mathrm{\Delta}\theta^{2}}{\mathrm{\Delta}\theta_{2}} = \left( \ \frac{I_{2}}{I_{1}} \right)^{2}\ or\ \frac{\mathrm{\Delta}\theta^{2}}{3} = \left( \ \frac{2I + I}{I} \right)^{2}$
or $\ \mathrm{\Delta}\theta_{2} = 9 \times 3 = 27℃.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.