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

A parallel plate capacitor connected to a battery develops a potential difference across its plates.
By integrating the equation relating voltage and current, an equation for the voltage across the capacitor at any given time is determined.
Capacitors possess memory, meaning their voltage depends on the past current flow.
The instantaneous power delivered to a capacitor is integrated over time to determine the energy stored in the capacitor.
An uncharged capacitor has a zero voltage. So, the energy stored in the capacitor is determined in terms of charge and capacitance, which represents the energy present in the electric field between the plates.
This energy can be retrieved as an ideal capacitor does not dissipate energy.
A non-ideal capacitor has a parallel-model leakage resistance, usually high enough to be neglected in most practical applications.
A capacitor can get charged when connected to a battery but acts as an open circuit to DC voltage.
The voltage across a capacitor is always continuous and cannot change abruptly.

energy stored in capacitors

A parallel plate capacitor, when connected to a battery, develops a potential difference across its plates. This potential difference is key to the operation of the capacitor, as it determines how much electrical energy the capacitor can store.
By integrating the equation that relates voltage and current in a capacitor, one can derive an equation for the voltage across the capacitor at any given time. This equation is crucial in understanding and predicting the behavior of capacitors in electronic circuits.
One interesting property of capacitors is that they possess a kind of memory. The voltage across a capacitor at any moment depends on the past flow of current through it. This means that capacitors can &#34;remember&#34; their charging and discharging history, which can be useful in various applications such as memory storage in computers.
The instantaneous power delivered to a capacitor can be used to determine the amount of energy stored in the capacitor. If we consider an uncharged capacitor at time equals minus infinity, it has zero voltage. This means that the energy stored in the capacitor can be determined in terms of charge and capacitance. This represents the energy present in the electric field between the plates.
This stored energy can be retrieved in terms of power since an ideal capacitor does not dissipate energy. However, real-world capacitors are not ideal. A non-ideal capacitor has a parallel-model leakage resistance, but this is usually high enough to be neglected in most practical applications.
A unique characteristic of capacitors is that they act as an open circuit to direct current (DC) voltage but can get charged when connected to a battery. This property allows capacitors to block DC while letting alternating current (AC) pass.
Another important feature of capacitors is that the voltage across them is always continuous and cannot change abruptly. This behavior is essential in many applications, such as smoothing out voltage in power supplies and filtering out noise in signal processing.
In conclusion, understanding capacitors, their properties, and their behavior in circuits is a fundamental aspect of electronics. It enables engineers to design and construct complex electronic systems that are integral to modern life.

A parallel plate capacitor connected to a battery develops a potential difference across its plates.
By integrating the equation relating voltage and ...

Education

JoVE Core

Electrical Engineering

Unit 1

Energy Storage Elements

KEY TERMS AND CONCEPTS

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...

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

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

P-PS2-5

Power and Energy

Energy is the total work required to drive the current through the circuit.
A rise in voltage results in more work done, passing more current, resulting ...

Energy and Work

Source: Ketron Mitchell-Wynne, PhD,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of ...

First Law of Thermodynamics

A change in the internal energy of a system depends on the the net heat transfer into the system and the net work done by the system. The first law of ...

first-law-of-thermodynamics-problem-solving

First Law Of Thermodynamics: Problem-Solving

The first law of thermodynamics states that the change in internal energy of the system is equal to the net heat transfer into the system minus the net ...

conservation-of-energy-approach-to-system-analysis

Conservation of Energy Approach to System Analysis

Source: Ricardo Mejia-Alvarez and Hussam Hikmat Jabbar, Department of Mechanical Engineering, Michigan State University, East Lansing, MI
The purpose of ...

Cyclic Processes And Isolated Systems

A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a ...

Isothermal Processes

A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to ...

Isochoric and Isobaric Processes

A thermodynamic process that occurs at constant volume is called an isochoric process. According to the first law of thermodynamics, heat supplied or ...

Create a computational model to calculate the change in the energy of one component in a system when the change in energy of the other component(s) and energy flows in and out of the system are known. 

Clarification statement: Emphasis is on explaining the meaning of mathematical expressions used in the model. 

Assessment Boundary: Assessment is limited to basic algebraic expressions or computations; to systems of two or three components; and to thermal energy, kinetic energy, and/or the energies in gravitational, magnetic, or electric fields.

HS-PS3-1

The universe is composed of matter in different forms, and all forms of matter contain energy.&#160; The different forms of energy on Earth originate from ...

Gravitational Potential Energy

Potential energy is not just a property of each object, but also a property of the interactions between objects in a chosen system. For each type of ...

Types of Potential Energy

Potential energy is also known as energy at rest or stored energy. Common types of potential energy include the gravitational potential energy stored in ...

Types of Kinetic Energy

The amount of kinetic energy of an object depends on its mass and speed. Consider two balls of different masses rolling down an inclined plane at the same ...

Kinetic Energy - I

It&#8217;s plausible to suppose that the greater the velocity of a body, the greater effect it could have on other bodies. This does not depend on the ...

Kinetic Energy - II

The kinetic energy of a particle is one-half of the product of the particle&#8217;s mass and the square of its speed. Note that just as Newton&#8217;s ...

Work-energy Theorem

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

Develop and use models to illustrate that energy at the macroscopic scale can be accounted for as a combination of energy associated with the motions of particles (objects) and energy associated with the relative position of particles (objects). 

Clarification statement: Examples of phenomena at the macroscopic scale could include the conversion of kinetic energy to thermal energy, the energy stored due to position of an object above the earth, and the energy stored between two electrically-charged plates. Examples of models could include diagrams, drawings, descriptions, and computer simulations.

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

Electric Generator: Alternator

Electric generators induce an emf by rotating a coil in a magnetic field. A simple alternator is an AC generator that creates electrical energy that ...

Dye-sensitized Solar Cells

Source: Tamara M. Powers, Department of Chemistry, Texas A&#38;M University
Today&#39;s modern world requires the use of a large amount of energy. While ...

Design, build, and refine a device that works within given constraints to convert one form of energy into another form of energy. 

Clarification statement: Emphasis is on both qualitative and quantitative evaluations of devices. Examples of devices could include Rube Goldberg devices, wind turbines, solar cells, solar ovens, and generators. Examples of constraints could include use of renewable energy forms and efficiency. 

Assessment Boundary: Assessment for quantitative evaluations is limited to total output for a given input. Assessment is limited to devices constructed with materials provided to students.

HS-PS3-3

Heat Flow and Specific Heat

Heat is a type of energy transfer that is caused by a temperature difference, and it can change the temperature of an object. Since heat is a form of ...

Calorimetry

When objects at different temperatures are placed in contact with each other but isolated from everything else, they attain thermal equilibrium. A ...

statements-of-the-second-law-of-thermodynamics

Statements of the Second Law of Thermodynamics

The second law of thermodynamics can be stated in several different ways, and all of them can be shown to imply the others. The Clausius&#8217; statement ...

entropy-and-the-second-law-of-thermodynamics

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The ...

Thermodynamic Systems

A thermodynamic system is a set of objects whose thermodynamic properties are of interest. The system is considered to be embedded in its surroundings or ...

Work Done During Volume Change

In mechanics, work is done on an object when the force acting on it displaces the object. In thermodynamics, work done on a system can be estimated when ...

Path Between Thermodynamics States

Consider the two thermodynamic processes involving an ideal gas that are represented by paths AC and ABC in Figure 1:

In the first process for path A to ...

Heat and Free Expansion

The work done by a thermodynamic system depends not only on the initial and final states but also on the intermediate states&#8212;that is, on the path. ...

Internal Energy

The internal energy of a thermodynamic system is the sum of the kinetic and potential energies of all the molecules or entities in the system. The kinetic ...

Plan and conduct an investigation to provide evidence that the transfer of thermal energy when two components of different temperature are combined within a closed system results in a more uniform energy distribution among the components in the system (second law of thermodynamics). 

Clarification statement: Emphasis is on analyzing data from student investigations and using mathematical thinking to describe the energy changes both quantitatively and conceptually. Examples of investigations could include mixing liquids at different initial temperatures or adding objects at different temperatures to water. 

Assessment Boundary: Assessment is limited to investigations based on materials and tools provided to students.

HS-PS3-4

Maxwell's Equation Of Electromagnetism

James Clerk Maxwell (1831&#x2013;1879) was one of the major contributors to physics in the nineteenth century. Although he died young, he made major ...

Magnetic Force

In addition to the electric forces between electric charges, moving electric charges exert magnetic forces on each other. A magnetic field is created by a ...

Magnetic Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Magnetic fields can be ...

Electric Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
An electric field is generated ...

Electric Charge in a Magnetic Field

Source: Andrew Duffy, PhD, Department of Physics, Boston University, Boston, MA
This experiment duplicates J.J. Thomson's famous experiment at the end of ...

Electric Potential Energy

When an electric field accelerates a free positive charge q, it is given kinetic energy. The process is analogous to an object accelerated by a ...

Develop and use a model of two objects interacting through electric or magnetic fields to illustrate the forces between objects and the changes in energy of the objects due to the interaction. 

Clarification statement: Examples of models could include drawings, diagrams, and texts, such as drawings of what happens when two charges of opposite polarity are near each other. 

Assessment Boundary: Assessment is limited to systems containing two objects.

HS-PS3-5

Capacitor Voltage and Charge Behavior

Description

Transcript

Tags

More videos by Standards