Question #43371

A resistor of constant heat capacity $C_h$ is connected across an ideal DC voltage source $V$. The resistance varies with temperature $T$ as $R(T) = R_0 [1 + \alpha (T - T_{env})]$, where $R_0$ is the resistance at the environment temperature $T_{env}$, and $\alpha > 0$ is the temperature coefficient of resistance. At $t=0$, the resistor is at an initial temperature $T_i$ ($T_i > T_{env}$) and loses heat to the environment according to Newton's Law of Cooling. The rate of heat loss is given by $P_{loss} = \lambda (T - T_{env})$, where $\lambda$ is a constant. Let $I_0$ and $R_i$ be the current and resistance at $t=0$, respectively, and let $\Delta T_i = T_i - T_{env}$. Which of the following expressions correctly gives the initial rate of change of current, $\left. \frac{dI}{dt} \right|_{t=0}$?