Q.
A constant current $i$ is passed through a resistor. Taking the temperature coefficient of resistance into account, indicate which of the plots shown in figure best represents the rate of production of thermal energy in the resistor
A) $a$
B) $b$
C) $c$
D) $d$
Explanation
(d) Thermal energy is resistor is $U = i^{2}Rt$
$R = R_{0}(1 + \alpha\theta) \Rightarrow U = i^{2}R_{0}(1 + \alpha\theta)t\ \ \lbrack where\ \theta = temp\rbrack$
So $\frac{dU}{dt} = i^{2}R_{0}(1 + \alpha\theta)$
With time temperature increases, hence $dU/dt$ increases. This is best shown by curve $(d)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.