4.2.AC CAPACITOR CIRCUITS814.2AC capacitor circuitsCapacitors do not behave the same as resistors. Whereas resistors allow a ﬂow of electrons throughthem directly proportional to the voltage drop, capacitors oppose changes in voltage by drawingor supplying current as they charge or discharge to the new voltage level. The ﬂow of electrons“through” a capacitor is directly proportional to the rate of change of voltage across the capacitor.This opposition to voltage change is another form of reactance, but one that is precisely opposite tothe kind exhibited by inductors.Expressed mathematically, the relationship between the current “through” the capacitor andrate of voltage change across the capacitor is as such:i = CdedtThe expression de/dt is one from calculus, meaning the rate of change of instantaneous voltage(e) over time, in volts per second. The capacitance (C) is in Farads, and the instantaneous current(i), of course, is in amps. Sometimes you will ﬁnd the rate of instantaneous voltage change overtime expressed as dv/dt instead of de/dt: using the lower-case letter “v” instead or “e” to representvoltage, but it means the exact same thing. To show what happens with alternating current, let’sanalyze a simple capacitor circuit: (Figure 90,4.4)CETIVCICET = ECI = ICECIC-90°Figure 4.4: Pure capacitive circuit: capacitor voltage lags capacitor current by 90oIf we were to plot the current and voltage for this very simple circuit, it would look somethinglike this: (Figure 90,4.5)Time +-e =i =Figure 4.5: Pure capacitive circuit waveforms.Remember, the current through a capacitor is a reaction against the change in voltage across it.Therefore, the instantaneous current is zero whenever the instantaneous voltage is at a peak (zero