Capacitor Discharge

The capacitance of a capacitor is measured in Farad and is the amount of energy it can store. Capacitors are used as crucial components of electrical circuits in many modern devices, including pacemakers, mobile phones, and computers.

Capacitors are commonly used to store electrical energy and release it when needed. They typically feature in combination with other circuit components to produce a filter that allows some electrical impulses to pass while blocking others.

How does a capacitor discharge?

Capacitors have two conductive plates separated by an insulator material. When the capacitor is charging, the following two steps below occur in the order in which they are listed:

Figure 1. A charged capacitor.

When the capacitor is discharging, the electron excess on the negatively charged plate starts to flow to the positively charged plate, which causes the capacitor to create an electron flow in the circuit and act as a voltage source for a period of time. This electron flow stops when the potential difference between the plates comes down to zero, which means that both plates are neutral at that point, and the charge that the capacitor was holding has been given back to the circuit.

How does a capacitor’s discharge behave in AC and DC circuits?

A capacitator’s discharge behaviour depends on whether it is found in an AC or a DC circuit.

In DC circuits, the capacitor charges and discharges only once. To understand the concept better, take a look at the circuit below.

Figure 2. A simple capacitor circuit.

Figure 3. A simple capacitor circuit.

Right after we move the switch to position 3, electron flow from the capacitor starts. Since it is in the opposite direction to the electron flow that was happening when the capacitor was charging, the ammeter’s indicator for a short time turns in the opposite direction before going back to zero. This load flow ends when the charge of the two plates of the capacitor is at the same level, which indicates that the capacitor has discharged.

Since the capacitor in the circuit in Figure 2 is short-circuited, the time period while the electron flow is present is very short. To increase this time period and use the capacitor as a source for a longer time, resistors need to be connected to the circuit since they resist current flow.

Figure 4. The voltage change of a capacitor during discharge.

As you can see, in DC circuits, we speak of the temporary state when the capacitor is discharging and the voltage level goes down to zero. When the capacitor is fully discharged, we speak of the steady state. This is the main difference between how capacitors behave in DC and AC circuits.

Figure 5. The current change of a capacitor during discharge.

In this figure, Ic is the current flowing through the capacitor, -V/R is the value of the current flowing through the capacitor when it is fully charged, and t is time.

You can see that the value of the current is starting to reach zero from a negative value. This is because the electron flow is in the opposite direction to the direction it was while the capacitor was charging. The direction of the current flow is, of course, also different.

After the capacitor is discharged, unless we move the switch to position 1, the charge of the capacitor and the current going through the circuit will remain zero.

The capacitor’s discharging behaviour in AC circuits

Whereas a capacitator in a DC circuit discharges only once, in an AC circuit, it charges and discharges continuously. The current flow is also different compared to a DC circuit, where it flows in one direction until the capacitor is discharged and then stops. In an AC circuit, by contrast, current flows in both directions continuously.

Figure 6. In AC circuits, a capacitor’s current and voltage have a 90-degree phase difference.

In this figure, V(t) is the voltage depending on time, i(t) is the current depending on time, V_m is the peak value of the voltage of the capacitor, I_m is the peak value of the alternative current going through the capacitor, and θ is the phase difference between the voltage and the current of the capacitor.

To understand the concept better, we will look at it in different parts of a period. Normally, there are four parts where the capacitor behaves differently: 0-π / 2, π / 2-π, π -3π / 2, and 3π / 2-2π. Let’s say the phase angle is a. In the π/2<a<π and the 3π/2<a<2π periods, the capacitor is discharging while in the other two periods, it is charging.

The π/2 <a <π period

Figure 7. Capacitor’s discharge in AC circuits (Diagram 1).

In this figure, Vt is the AC voltage source, which depends on time, while \(V_{max} \cdot \sin(\omega t)\) is the function defining its sinusoidal behaviour.

Because the capacitor’s voltage is at its peak at the a=3π/2 point, the load will be at its maximum as well. And because the capacitor is completely charged, there will be no current flowing through it at this precise moment. As a result, the current value is i = 0.

Figure 8. Capacitor’s discharge in AC circuits (Diagram 2).

Notice how the bottom plate of the capacitor is now charged. This is because in the π <a <3π/2 period, the current that the AC source generates was flowing in the opposite direction, causing the capacitor to charge in the opposite direction.

The voltage of the source decreases after a=3π/2, implying that the voltage of the capacitor will drop as well, and the capacitor will begin to discharge. As we get closer to the 2π point, the rate of change of the voltage (dV/dt) and the current both increase.

The value of the current is at its maximum at point 2π, and the value of the AC source voltage is zero. The load on the capacitor (q) is also 0 at this moment since it has been discharged.

When a basic circuit like the one we just studied doesn’t include a resistor, it is impossible to calculate the time it takes a capacitor to discharge. However, there is no need to calculate it because the capacitator will discharge very quickly. So, to calculate the time it takes a capacitor to discharge, we need an RC circuit. Let’s consider the example below.