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.

Get started

Review generated flashcards

Sign up for free
You have reached the daily AI limit

Start learning or create your own AI flashcards

StudySmarter Editorial Team

Team Capacitor Discharge Teachers

  • 10 minutes reading time
  • Checked by StudySmarter Editorial Team
Save Article Save Article
Contents
Contents

Jump to a key chapter

    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.

    Capacitor Discharge. Charged capacitor. StudySmarterFigure 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.

    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.

    Capacitor Discharge. Simple capacitor circuit. StudySmarterFigure 2. A simple capacitor circuit.

    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.

    Capacitor Discharge. Simple capacitor circuit. StudySmarterFigure 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.

    Capacitor Discharge. Capacitor discharge graph. StudySmarterFigure 4. The voltage change of a capacitor during discharge.

    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.

    Capacitor Discharge. Capacitor discharge graph. StudySmarterFigure 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.

    Capacitor Discharge. Phase difference between capacitor’s current and voltage. StudySmarterFigure 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, 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: \(q = Q_m = V_m \cdot C\), where q is the load, Qm is the maximum load, Vm is the peak value of the AC source, and C is capacitance.

    Capacitor discharge. Capacitor discharge in AC circuits. StudySmarterFigure 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 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.

    Capacitor Discharge. Capacitor discharge diagram. StudySmarterFigure 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.

    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?

    Capacitor Discharge. RC circuit. StudySmarterFigure 9. A simple RC circuit.

    The time it takes for the capacitor to discharge is 5T, where T is the time constant that can be calculated as:

    \[\tau = R \cdot C\]

    Entering the known values, we get:

    \[\tau = 100[\Omega] \cdot 0.02[F] = 2[s]\]

    And, as already said, the discharge time equals 5T. This gives us:

    \[5 \cdot \tau = 2[s]\cdot 5 = 10 [s]\]

    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.
    Frequently Asked Questions about Capacitor Discharge

    How long does it take a capacitor to discharge?

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

    What causes a capacitor to discharge?

    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.

    What is a capacitor 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.

    How do you discharge a capacitor?

    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. 

    When do capacitors discharge?

    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. 

    Save Article

    Test your knowledge with multiple choice flashcards

    Which of the following is the unit for capacitance?

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

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

    Next

    Discover learning materials with the free StudySmarter app

    Sign up for free
    1
    About StudySmarter

    StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.

    Learn more
    StudySmarter Editorial Team

    Team Physics Teachers

    • 10 minutes reading time
    • Checked by StudySmarter Editorial Team
    Save Explanation Save Explanation

    Study anywhere. Anytime.Across all devices.

    Sign-up for free

    Sign up to highlight and take notes. It’s 100% free.

    Join over 22 million students in learning with our StudySmarter App

    The first learning app that truly has everything you need to ace your exams in one place

    • Flashcards & Quizzes
    • AI Study Assistant
    • Study Planner
    • Mock-Exams
    • Smart Note-Taking
    Join over 22 million students in learning with our StudySmarter App
    Sign up with Email