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# Capacitor Discharge Save Print Edit
Capacitor Discharge
• Astrophysics • Atoms and Radioactivity • Electricity • Energy Physics • Engineering Physics • Fields in Physics • Force • Further Mechanics and Thermal Physics • Magnetism • Measurements • Mechanics and Materials • Medical Physics • Nuclear Physics • Particle Model of Matter • Physical Quantities and Units • Physics of Motion • Radiation • Space Physics • Turning Points in Physics • Waves Physics 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:

1. A potential difference between the two conductive plates begins to rise as a result of the electrical field created by the source in the circuit. One of the plates gains excess electrons from the other plate because the electrical field of the source is pushing the electrons from the plate whose positive pole is directed towards.
2. Once the charging is completed, one of the plates has a positive charge, while the other has a negative charge. Figure 1. A charged capacitor. Source: Oğulcan Tezcan, StudySmarter.

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.

### The capacitor’s discharging behaviour in DC circuits

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, Source: Oğulcan Tezcan, StudySmarter.

In this circuit, the ammeter (A) indicates the value of current flowing through the capacitor, while the voltmeter (V) indicates the potential difference between the plates. When we move the switch to position 1, the capacitor charges. The upper plate is charged positively because the electric field of the source pushed the electrons in the upper plate into the bottom plate, which means that the bottom plate is charged negatively. If we then move the switch to position 3, the capacitor begins to discharge. Figure 3. A simple capacitor circuit. Source: Oğulcan Tezcan, StudySmarter.

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. Source: Oğulcan Tezcan, StudySmarter.

In the figure above, Vc is the voltage value of the capacitor, V is the voltage value of the capacitor when it is fully charged, and t is time.

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. Source: Oğulcan Tezcan, StudySmarter.

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. Source: Manuel R. Camacho, StudySmarter.

In this figure, V(t) is the voltage depending on time, i(t) is the current depending on time, Vm is the peak value of the voltage of the capacitor, Im 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

As you can see in figure 6, at a = π/2, the current is zero, and the capacitor’s voltage is at its maximum value (V = Vm). This also indicates that the load on the capacitor is at its maximum: q = Qm = Vm ⋅ C, where q is the load, Qm is the maximum load, Vm is the peak value of the AC source, and C is capacitance. Figure 7. Capacitor’s discharge in AC circuits (Diagram 1). Source: Oğulcan Tezcan, StudySmarter.

In this figure, Vt is the AC voltage source, which depends on time, while Vmax ⋅ sin(wt) is the function defining its sinusoidal behaviour.

Because the voltage value of the AC source is decreasing after a=π/2, the capacitor’s voltage will decrease as well. This also implies that the capacitor’s load will decrease, forcing the electron flow to reverse direction as the excess electrons in the bottom plate go to the upper plate. That is the reason why the current’s direction changes. As we get closer to a=π, the voltage of the AC source begins to change rapidly, causing the current value to rise. The capacitor’s voltage value is 0 at the a=π point, indicating that it has discharged.

### The 3π/2 <a <2π period

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). Source: Oğulcan Tezcan, StudySmarter.

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.

## How long does it take a capacitor to discharge?

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.

In the circuit below, the capacitor is fully charged with 10 volts. If we close the switch at time t = 0, how much time will it take for the capacitor to fully discharge? Figure 9. A simple RC circuit. Source: Oğulcan Tezcan, StudySmarter.

The time it takes for the capacitor to discharge is 5T, where T is the time constant that can be calculated as: Entering the known values, we get: And, as already said, the discharge time equals 5T. This gives us: ## Capacitor Discharge - Key takeaways

• There is a difference in how capacitors operate in DC and AC circuits since the voltage levels are steady in DC and constantly changing in AC.
• Capacitator discharge happens when the electric field of the source surrounding the capacitor disappears, causing the start of the electron flow from the conductive plates to the circuit.
• The time it takes for a capacitor to discharge is 5T, where T is the time constant.
• There is a need for a resistor in the circuit in order to calculate the time it takes for a capacitor to discharge, as it will discharge very quickly when there is no resistance in the circuit.
• In DC circuits, there are two states when a capacitor is discharging. The first is the temporary state, which is while the capacitor is discharging. The second is the steady state, which is when the capacitor is fully discharged.

The time it takes for a capacitor to discharge is 5T, where T is the time constant.

When the capacitor is fully charged and the electrical field from the source surrounding the capacitor goes down to zero, it causes an electron flow from the conductive plates of a capacitor to the circuit, which then causes the capacitor to discharge.

A capacitor discharge is a situation that occurs when the electrical field from the voltage source around the capacitor goes down to zero, leading to an electron flow, which causes the potential difference between the two conductive plates to reach zero. This is possible when the charges of the two conductive plates are the same.

You can discharge a capacitor by simply connecting it to a circuit without a source, or you can short-circuit the poles of the capacitor using a conducting material.

Capacitors discharge when another path in the circuit that allows the charges to flow to each other is created. This causes the charges to flow out of the capacitor, and the capacitor becomes discharged after some time.

## Final Capacitor Discharge Quiz

Question

Which of the following is the unit for capacitance?

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Question

Which of the following causes the current flow to change its direction when a capacitor is discharging?

Electron flow changing its direction.

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Question

Why does a capacitor behave differently in AC circuits and DC circuits?

Because the voltage levels are stable in DC and continuously changing in AC.

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Question

When does a capacitor begin to discharge?

When the electric field surrounding the capacitor disappears.

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Question

What is the behaviour of a capacitor’s voltage compared to that of the source in an AC circuit?

It is the same as the AC source’s voltage.

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Question

In which circuits can we calculate the time it takes a capacitor to discharge?

In RC circuits.

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Question

What happens to the current flow when the electron flow’s direction changes?

It also changes its direction.

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If there is no resistor connected to the circuit, how long does a capacitor take to discharge?

A very short time.

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Question

What is the name given to the period when a capacitor is discharging?

Temporary state.

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Question

What is the name given to the period when a capacitor is fully discharged?

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Question

In which direction does the current flow through a capacitor in AC circuits?

In both directions.

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How much phase difference do the capacitor’s current and voltage have in AC circuits?

A 90-degree phase difference.

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Question

How does the current flow behave on a capacitor when it’s fully charged?

It can’t go through the capacitor.

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Question

What is the equation for finding the load of a capacitor?

Q = U * C.

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Question

What is the equation for finding the time constant?

T = R * C.

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