Figure 26.2 shows the resistor voltage, capacitor voltage, circuit current, and capacitor charge in the
charging RC circuit as a function of time. The capacitor is initially uncharged, and switchSis closed at time
tD 0. Shortly after the switchSis closed, a large current flows through the circuit, the voltage across the
resistorRis equal to the battery voltageV, and the voltage across the capacitor is zero. At time DRC
after the switch is closed, the voltage across the resistor has decreased to1=eD0:368of the battery voltage;
the voltage across the capacitor has increased to 1 1=eD0:632of the battery voltage; the current has
decreased to1=eof its initial value; and the charge on each of the plates of the capacitor has increased to
1 1=eof its maximum capacity.
Mathematically, the voltage across the resistorVR, the voltage across the capacitorVC, the current in the
circuitI, and the charge on each capacitor plateQcan be shown to be
VR.t/DVet= (26.2)
VC.t/DV.1et=/ (26.3)
I.t/D.V=R/et= (26.4)
Q.t/DCV.1et=/ (26.5)As timet!1, current will stop flowing in the circuit, the capacitor will have reached its maximum
charge, the voltage across the resistor will be zero, and the voltage across the capacitor will equal the battery
voltage.
Figure 26.2: Plots vs. time for a charging RC circuit. (a) Resistor voltage vs. time; (b) capacitor voltage vs.
time; (c) circuit current vs. time; and (d) charge on the capacitor vs. time. The capacitor is initially uncharged,
and the switchSis closed at timetD 0.
26.2 Discharging RC Circuit
Figure 26.3 shows a discharging RC circuit. There is no battery in this circuit; instead, we have a capacitor
Cthat is initially fully charged to potentialVthat is connected in series with a resistorR. When switchSis
closed at timetD 0 , the voltage across the resistor and capacitor, the circuit current, and the capacitor charge
alldecrease exponentially, and reach1=eof their initial value in time DRC. As timet!1, the current,
all voltages, and the capacitor charge will all dwindle to zero. Mathematically, the voltage across the resistor
VR, the voltage across the capacitorVC, the current in the circuitI, and the charge on each capacitor plateQ