A constant current i is passed through a resistor. Taking the tem… - Vidyadip

MCQ

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
$c$
✓
$d$

✓

Answer

Correct option: D.

$d$

(d) Thermal energy in resistor is $U=i^2 R t$where $R=R_0(1+\alpha t) \Rightarrow U=i^2 R_0(1+\alpha t) t=i^2 R_0 t+i^2 R_0 t^2$So $\frac{d U}{d t}=i^2 R_0(1+\alpha t)$With the time temperature increases, hence $d U / d t$ increases. This is best shown by curve $(d)$.

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