Name: capacitor voltage and charge behavior
Uploaded: 2024-04-11T12:48:38.000Z
Duration: 1 min 10 s
Channel: JoVE

K12 Standards

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

High School

Physical Science

Energy

HS-PS3-2

Energy Stored in Capacitors

Конденсатор с параллельными пластинами, подключенный к батарее, развивает разность потенциалов на своих пластинах.
Путем интегрирования уравнения, связывающего напряжение и ток, определяется уравнение для напряжения на конденсаторе в любой момент времени.
Конденсаторы обладают памятью, то есть их напряжение зависит от протекания тока в прошлом.
Мгновенная мощность, подаваемая на конденсатор, интегрируется во времени для определения энергии, хранящейся в конденсаторе.
Незаряженный конденсатор имеет нулевое напряжение. Таким образом, энергия, накопленная в конденсаторе, определяется с точки зрения заряда и емкости, которая представляет собой энергию, присутствующую в электрическом поле между пластинами.
Эту энергию можно восстановить, так как идеальный конденсатор не рассеивает энергию.
Неидеальный конденсатор имеет сопротивление утечке по параллельной модели, обычно достаточно высокое, чтобы им можно было пренебречь в большинстве практических применений.
Конденсатор может заряжаться при подключении к аккумулятору, но действует как разомкнутая цепь постоянного напряжения.
Напряжение на конденсаторе всегда непрерывно и не может резко изменяться.

Энергия, запасенная в конденсаторах

Конденсатор с параллельными пластинами при подключении к батарее создает разность потенциалов на своих пластинах. Эта разность потенциалов - очень важный параметр конденсатора, поскольку она определяет, сколько электрической энергии может хранить конденсатор.

Интегрируя уравнение, связывающее напряжение и ток в конденсаторе, можно получить уравнение для напряжения на конденсаторе в любой момент времени. Это уравнение имеет решающее значение для понимания и прогнозирования поведения конденсаторов в электронных схемах.

Одним из интересных свойств конденсаторов является то, что они обладают своего рода памятью. Напряжение на конденсаторе в любой момент зависит от протекавшего через него тока. Это означает, что конденсаторы могут «запоминать» историю своей зарядки и разрядки, что может быть полезно в различных приложениях, таких как запоминающие устройства в компьютерах.

Мгновенную мощность, подаваемую на конденсатор, можно использовать для определения количества энергии, запасенной в конденсаторе. Если рассматривать незаряженный конденсатор в момент времени, равный минус бесконечности, то он имеет нулевое напряжение. Это означает, что энергию, запасенную в конденсаторе, можно определить через заряд и электроёмкость. Это представляет собой энергию, присутствующую в электрическом поле между пластинами.

Эту накопленную энергию можно извлечь в виде мощности, поскольку идеальный конденсатор не рассеивает энергию. Однако реальные конденсаторы не идеальны. Неидеальный конденсатор имеет сопротивление утечки параллельной модели, но оно обычно достаточно велико, чтобы им можно было пренебречь в большинстве практических приложений.

Уникальной характеристикой конденсаторов является то, что они действуют как разомкнутая цепь для напряжения постоянного тока (DC), но могут заряжаться при подключении к батарее. Это свойство позволяет конденсаторам блокировать постоянный ток, пропуская при этом переменный ток (AC).

Еще одной важной особенностью конденсаторов является то, что напряжение на них всегда непрерывно и не может резко меняться. Такое поведение важно во многих приложениях, таких как сглаживание напряжения в источниках питания и фильтрация шума при обработке сигналов.

В заключение, понимание конденсаторов, их свойств и поведения в цепях является фундаментальным аспектом электроники. Это позволяет инженерам проектировать и конструировать сложные электронные системы, которые являются неотъемлемой частью современной жизни.

Конденсатор с параллельными пластинами, подключенный к батарее, развивает разность потенциалов на своих пластинах.
Путем интегрирования уравнения, связывающего напряжение и ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Energy Storage Elements

Элементы хранения энергии

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

capacitor voltage and charge behavior

Capacitor voltage and charge behavior depend on how a parallel plate capacitor connects to a battery. When the battery is attached, a potential difference forms across the plates. That voltage determines how much electrical energy the capacitor can store.

The voltage across a capacitor can be found by integrating the equation that links voltage and current. That relationship lets students predict the voltage at any moment during charging or discharging. It also shows why a capacitor keeps a record of its past current flow. In that sense, the capacitor has a kind of memory.

This memory effect means the voltage at one moment depends on what happened earlier in the circuit. That idea is useful in applications such as memory storage in computers. The instantaneous power delivered to the capacitor can then be used to calculate the energy stored in it.

If the capacitor starts uncharged at time equals minus infinity, its initial voltage is zero. From there, the stored energy can be written in terms of charge and capacitance. That energy is the energy in the electric field between the plates. An ideal capacitor can give that energy back because it does not dissipate energy.

Real capacitors are not perfect. A non-ideal capacitor has a parallel-model leakage resistance, but this resistance is usually high enough to ignore in most practical cases. Capacitors also act as an open circuit for direct current, yet they can still charge when connected to a battery. This is why they block DC while allowing alternating current to pass.

Another key feature is that capacitor voltage changes continuously. It cannot jump suddenly. This property is important in power supplies, where capacitors smooth voltage, and in signal processing, where they help filter out noise. Understanding these behaviors is a basic part of electronics and helps engineers build modern electronic systems.

Capacitor Voltage and Charge Behavior

capacitors

Capacitor Charge and Discharge

Capacitors store electric energy and help control signals in devices like car radios. They work by holding charge on two parallel conducting plates with a dielectric, which is the insulating material between the plates. When a voltage source is connected, positive charge builds up on one plate and negative charge builds up on the other. This charge separation creates a potential difference, and it keeps increasing until it matches the source voltage. The electric field inside the capacitor...

energy stored in capacitors

Capacitor voltage and charge behavior depend on how a parallel plate capacitor connects to a battery. When the battery is attached, a potential difference forms across the plates. That voltage determines how much electrical energy the capacitor can store. The voltage across a capacitor can be found by integrating the equation that links voltage and current. That relationship lets students predict the voltage at any moment during charging or discharging. It also shows why a capacitor keeps a...

series and parallel capacitors

Capacitance in Series and Parallel

Capacitors in series and parallel affect a circuit in different ways. These arrangements change the total capacitance, which is the circuit's overall ability to store charge. Knowing the difference helps explain how a circuit responds to signals. When capacitors are connected in series to a battery, the plate tied to the battery's positive terminal becomes positively charged. The plate connected to the negative terminal becomes negatively charged. The other plates develop equal and opposite...

equivalent capacitance

Capacitors in Series and Parallel

Capacitors in series and parallel can be simplified by replacing the group with one equivalent capacitor. This equivalent capacitor stores the same charge as the original network when the same potential difference is applied. The idea helps make complex capacitor circuits easier to analyze. In a parallel connection, capacitors share the same voltage across each branch. The equivalent capacitance of N capacitors in parallel is the sum of their individual capacitances. This type of connection...

inductors

Inductors in Electric Circuits

Inductors are passive components used in electric circuits to store energy in a magnetic field. They are often made by coiling a wire around a magnetic core. This structure gives the component its inductive behavior and its ability to respond to changing current. When current flows through an inductor, the voltage across it is proportional to how quickly the current changes with time. This relationship is written using the passive sign convention, and the constant of proportionality is called...

energy stored in inductors

How Inductor Current Stores Magnetic Energy

An inductor stores energy in its magnetic field. That field is created by the current flowing through the coil. When the current stays steady, there is no measurable voltage across the inductor, so it behaves like a short circuit for direct current. The energy stored in an inductor is the total power delivered over time. It can be written as a function of inductance, L, and current, i, where the stored energy increases with the current in the coil. This relationship helps explain how much...

series and parallel inductors

Equivalent Inductance in Circuit Networks

Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage. For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is...

design example: automobile ignition system

design-example-automobile-ignition-system

Car Spark Coil Voltage Design Example

An automobile ignition system uses a spark plug and a spark coil to create the high voltage needed to ignite the fuel-air mixture in each cylinder. The spark plug has two electrodes with an air gap between them. When enough voltage appears across that gap, a spark forms and starts combustion. A 12-volt car battery does not create that spark by itself. The system uses an inductor, which is a component that resists rapid changes in current, to build a much larger voltage. In this ignition setup,...

key terms and concepts

Learn how capacitor voltage builds, how charge stores energy, and why capacitors block DC, pass AC, and smooth voltage in circuits.

Capacitor Voltage and Charge Behavior | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

Texas Essential Knowledge and Skills

Chemistry and Physics

IPC.6

IPC.6.A

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

Physics

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P-PS2-5

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HS-PS3-3

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HS-PS3-4

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HS-PS3-5

Capacitor Voltage and Charge Behavior

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