A constant current i is maintained in a resistor. Taking into...

The rate of thermal energy production in a resistor is given by $\dfrac{dU}{dt} = i^2 R$.

Since the current $i$ is constant, the rate of energy production is directly proportional to the resistance $R$.

As current flows through the resistor, its temperature $T$ increases due to Joule heating.

The resistance of a typical metallic resistor increases with temperature according to the relation $R = R_0[1 + \alpha(T - T_0)]$, where the temperature coefficient of resistance $\alpha > 0$.

Therefore, the resistance $R$ increases with time, which implies that $\dfrac{dU}{dt}$ also increases with time.

At $t = 0$, $\dfrac{dU}{dt} = i^2 R_0 > 0$, so the graph must start from a positive value on the y-axis.

Curve 'd' starts from a positive value and increases with time, making it the correct representation.