http://www.ck12.org Chapter 14. Electric Circuits Version 2
14.5 Charging and Discharging Capacitors (Transient)
When a capacitor is initially uncharged, it is very easy to increase the amount of charge on its plates. As charge
builds, the charge present repels new charge with more and more force. Due to this effect, the charging of a capacitor
follows a logarithmic curve. When a circuit passes current through a resistor into a capacitor, the capacitor eventually
Òfills upÓ andno more current flows across it. A typical RC circuit is shown below; when the switch is closed, the
capacitor discharges with an exponentially decreasing current:
Q(t) =Q 0 e−τt
[7] Discharge rate of a capacitor, whereτ=RCandQ 0 =VC ̇Q(t) =Q 0 ( 1 −e−τt
) [8] Charge rate of a capacitor, whereτ=RCandQ 0 =VC ̇I(t) =I 0 (e−τt
[9] Discharge and Charge rate for current, whereτ=RCandI 0 =V
R
Charging a capacitor involves moving charges through a potential difference; as we saw in the electricity chapter,
this results in electric potential energy being stored in the capacitor:
U=
1
2
CV^2 [10] Potential energy stored in a capacitor