Capacitor Charging and Discharging Simulation

About this experiment

Follow charge building on a capacitor through a resistor, then switch to a discharge run. Compare capacitor voltage, signed current and stored energy. Playback uses t divided by RC so a short and a long time constant can be inspected at the same visual pace; the physical elapsed time is always shown separately.

Learning goals

Interpret RC as the characteristic charging and discharge time
Compare capacitor voltage and current during charge and discharge
Relate capacitance and voltage to stored charge and energy
Use the 63 % and 37 % rule to read a time constant from a graph

How to use it

1In Charge mode, advance one time constant and compare capacitor voltage with the supply voltage.
2Double resistance and compare the physical time constant and initial current.
3Switch to Discharge mode. At one time constant, compare the remaining voltage with its initial value.
4Keep voltage fixed, double capacitance and compare stored charge, energy and the time constant.
5Read the capacitor voltage after 1, 2, 3, 4 and 5 time constants. What fraction of the supply is reached each time?

The model

τ = R C, u = t / τ

The time constant and normalized time

V_{C} = V_{0} (1 - e^{- u}), I = \frac{V _{0}}{R} e^{- u}

Charging an initially uncharged capacitor

V_{C} = V_{0} e^{- u}, I = - \frac{V _{0}}{R} e^{- u}

Discharge from V0, with current signed relative to the charging direction

Q = C V_{C}, E = \frac{1}{2} C V_{C}^{2}

Stored charge and capacitor energy

Assumptions

The circuit contains an ideal resistor and capacitor. Wire resistance, capacitor leakage, internal resistance and inductance are ignored.
A charge run begins with zero capacitor voltage; a discharge run begins with the selected initial voltage and the supply bypassed.
Moving dots show conventional current in the wires schematically. They are not electrons crossing the dielectric.
Playback advances by 0.5 time constants per second. The physical clock is u times RC; it can differ from screen time.

Try this in class

Q1What fraction of the supply voltage is reached after one charging time constant?
Q2Why does the discharge current have a negative sign in the readout?
Q3If capacitance doubles at a fixed voltage, how do charge, energy and RC change?
Q4A camera flash charges a capacitor for a few seconds and empties it in a millisecond. What does that tell you about the resistance in each circuit?
Q5Why do engineers often say a capacitor is fully charged after 5 time constants?

Frequently asked questions

Why does changing resistance not change the normalized voltage curve?

For an ideal RC circuit, voltage as a function of t/RC has the same exponential form. Resistance changes physical time and current, while the normalized graph remains unchanged.

Does current flow through the capacitor dielectric?

No conduction current crosses an ideal dielectric. Current in the external wires changes the charge on the plates. The particle markers are omitted in the gap between the plates.

Is the capacitor ever completely charged?

In the ideal model the voltage gets closer and closer to the supply without reaching it. After 5 time constants it is within 1 % of the supply, which is why 5RC is used as a practical rule.