The current, I, is the rate at which charges flow through the circuit, and is thus equal to rate at which charges accumulate on the capacitor: \begin{aligned} I=\frac{dQ}{dt}\end{aligned} Subs...The current, I, is the rate at which charges flow through the circuit, and is thus equal to rate at which charges accumulate on the capacitor: \begin{aligned} I=\frac{dQ}{dt}\end{aligned} Substituting this into the loop equation, we obtain a separable differential equation for the charge on the capacitor as a function of time, Q(t): \[\begin{aligned} \Delta V - IR - \frac{Q}{C} &= 0\\ \Delta V - \frac{dQ}{dt}R - \frac{Q}{C} &= 0\\ \Delta V - \frac{Q}{C} &= \frac{dQ}{dt}R\\ C\Delta V…
