Name: capacitors in series and parallel
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Equivalent Capacitance

3つのコンデンサグループが並列に接続され、これらのグループが互いに直列に接続されている複雑なコンデンサネットワークを考えてみましょう。この複雑な回路の端子間の等価容量を決定します。
これを解決するために、回路の下部にあるグループ(並列に接続された4つのコンデンサで構成されるグループ)が最初に分析されます。それらの静電容量の合計は、単一のコンデンサC3で表される等価静電容量を与えます。
次に、3つのコンデンサを並列に持つ中間グループを検討します。ここでも、それらの容量を合計すると、等価な容量C2が得られます。
最後に、2つのコンデンサが並列にある最上位のグループについて考えてみます。等価容量は計算され、1つのコンデンサC1で表されます。
現在、複素回路は直列に接続された3つのコンデンサに簡略化されています。
この直列の組み合わせの等価容量を決定するには、各容量の逆数の合計が取得され、等価容量の逆数になります。
項を並べ替えると、端子間の回路全体の等価容量が得られます。

等価静電容量

抵抗回路の研究から、直並列の組み合わせを採用することが回路を簡素化するための効果的な戦略として機能することが分かっています。 コンデンサは、直列構成または並列構成の 2 つの方法のいずれかで回路内に配置できます。 これらのコンデンサをバッテリーに接続する方法が、個々のコンデンサの電位降下と各コンデンサが蓄積できる電荷のサイズの両方に影響します。 これは、実行されている特定の接続の種類によって決まります。 このシナリオを単純化するために、コンデンサの組み合わせを単一の等価コンデンサで置き換えることができます。 この等価コンデンサは、同じ電位差にさらされた場合、元の組み合わせと同じ量の電荷を蓄積できます。

N 個のコンデンサが並列接続されている場合、それらはすべて同じ電圧を共有します。 このような構成の等価静電容量は次の式で与えられます。

<img alt="Equation1" src="/files/ftp_upload/15087/15087_PT_Equation_1.svg" style="text-align: center; height: 14px;">

並列接続された N 個のコンデンサの等価静電容量は、それぞれの個別の静電容量の合計に等しいことに注意することが重要です。

ここで、N 個のコンデンサが直列に相互接続されているシナリオに移ると、同じ電流 i が、したがってすべてのコンデンサに同じ電荷が流れることが観察されます。 この設定の等価静電容量は次のように表されます。

<img alt="Equation2" src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;">

並列構成とは対照的に、直列に接続されたコンデンサの等価静電容量は、各コンデンサの個別の静電容量の逆数の合計の逆数として計算されます。

3つのコンデンサグループが並列に接続され、これらのグループが互いに直列に接続されている複雑なコンデンサネットワークを考えてみましょう。...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Energy Storage Elements

エネルギー貯蔵素子

KEY TERMS AND CONCEPTS

主要用語と概念

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 increases the total ability of the circuit to store charge.

In a series connection, the same current flows through each capacitor, and the same charge passes through them. The equivalent capacitance for N capacitors in series is found from the reciprocal of the sum of the reciprocals of each capacitance. This result is different from the parallel case and gives a smaller effective capacitance.

Capacitors in Series and Parallel

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

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 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 capacitors behave in series and parallel, and how to find equivalent capacitance by adding capacitances in parallel or using reciprocals in series.

Capacitors in Series and Parallel | JoVE K12

JoVE Core 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Resistors In Series

A resistor is an ohmic device that limits the flow of charge in a circuit. Most circuits have more than one resistor. If several resistors are connected ...

Resistors In Parallel

Resistors are in parallel when one end of all the resistors are connected to a continuous wire of negligible resistance and the other end of all the ...

Combination Of Resistors

Electrical devices in any circuit can be connected either by series or parallel connections. Additionally, circuits can be connected involving both of ...

Energy Transfer in Chemical Reactions

Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ...

Capacitors

Car radios utilize capacitors to filter frequencies for clear signal reception.
Capacitors consist of two parallel conducting plates separated by a ...

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 ...

Series and Parallel Capacitors

Capacitors can be connected in series and/or parallel configurations within a circuit.
Consider the capacitors connected in series to a battery; the plate ...

Consider a complex capacitor network with three groups of capacitors connected in parallel, and these groups are then connected in series with each other. ...

Inductors

Inductors, often referred to as coils or chokes, play a crucial role in various electronics and power systems.
In essence, any conductor through which an ...

Energy Stored in Inductors

An inductor is designed to store energy in its magnetic field, which is generated by the current flowing through its coils.
When the current is constant, ...

Series and Parallel Inductors

Inductors connected in series and/or parallel configurations can be simplified to an equivalent single inductor.
Consider a series connection of inductors ...

Design Example: Automobile Ignition System

An automobile&#39;s ignition system includes an essential component, the spark plug, with two electrodes separated by an air gap. When high voltage is ...

Design and construct series and parallel circuits that model real-world circuits such as in-home wiring, automobile wiring, and simple electrical devices to evaluate the transfer of electrical energy

Magnetism

Magnets are commonly found in everyday objects, such as toys, hangers, elevators, doorbells, and computer devices. Experimentation on these magnets shows ...

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Flux

The magnetic flux measures the number of magnetic field lines passing through a given surface area. The SI unit for magnetic flux is the weber (Wb). ...

Induction

An emf is induced when the magnetic field in a coil is changed by pushing a bar magnet into or out of the coil. emfs of opposite signs are produced by ...

Faraday's Law

Faraday&#39;s law state that the induced emf is the negative change in the magnetic flux per unit of time. Any change in the magnetic field or change in ...

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 ...

DC Generator

An alternator converts mechanical energy into electrical energy that varies sinusoidally, resulting in AC current. Meanwhile, a DC generator converts ...

Design, evaluate, and refine a device that generates electrical energy through the interaction of electric charges and magnetic fields

IPC.6.B

Energy

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 ...

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 ...

Simple Harmonic Motion

Simple harmonic motion is the name given to oscillatory motion for a system where the net force can be described by Hooke&#39;s law. If the net force can ...

/files/media/science-education/science-education-thumbs/12762.jpg

Simple Pendulum

A simple pendulum consists of a small diameter ball suspended from a string, which has negligible mass but is strong enough to not stretch. In our daily ...

Frequency of Spring-Mass System

One interesting characteristic of the simple harmonic motion (SHM) of an object attached to a spring is that the angular frequency, and the period and ...

/files/media/science-education/science-education-thumbs/14718.jpg

Plan and conduct an investigation to provide evidence that energy is conserved within a closed system.

IPC.6.C

Mechanisms of Heat Transfer I

Just as interesting as the effects of heat transfer on a system are the methods by which the heat transfer occur. Whenever there is a temperature ...

Mechanisms of Heat Transfer II

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the ...

conduction-convection-and-radiation-problem-solving

Conduction, Convection and Radiation: Problem Solving

There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting ...

Investigate and demonstrate the movement of thermal energy through solids, liquids, and gases by convection, conduction, and radiation such as weather, living, and mechanical systems.

IPC.6.D

Travelling Waves

A wave is a disturbance that propagates from its source, repeating itself periodically, and is typically associated with simple harmonic motion. ...

Wave Parameters

The simplest mechanical waves are associated with simple harmonic motion and repeat themselves for several cycles. These simple harmonic waves can be ...

Velocity and Acceleration of a Wave

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which ...

Speed of a Transverse Wave

The speed of a wave depends on the characteristics of the medium. For example, in the case of a guitar, the strings vibrate to produce the sound. The ...

/files/media/science-education/science-education-thumbs/14722.jpg

Kinetic and Potential Energy of a Wave

All forms of waves carry energy; this is directly visualized in nature. For instance, the waves of earthquakes are so intense that they can shake huge ...

Energy and Power of a Wave

The total energy associated with a wavelength is the sum of the potential energy and the kinetic energy. The average rate of energy transfer associated ...

Electromagnetic Waves

James Clerk Maxwell formulated a single theory combining all the electric and magnetic effects scientists knew during that time, calling the phenomena his ...

propagation-speed-of-electromagnetic-waves

Propagation Speed of Electromagnetic Waves

Electromagnetic waves are consistent with Ampere&#39;s law. Assuming there is no conduction current Ampere&#39;s law is given as:


Consider a plane ...

Electromagnetic Waves in Matter

Electromagnetic waves can travel in the vacuum as well as in matter. For example light, which is an electromagnetic wave, can travel through air, water, ...

Energy Carried By Electromagnetic Waves

Anyone who has used a microwave oven knows there is energy in electromagnetic waves. Sometimes, this energy is obvious, such as in the summer sun&#39;s ...

Intensity Of Electromagnetic Waves

The energy transport per unit area per unit time, or the Poynting vector, gives the energy flux of an electromagnetic wave at any specific time. For a ...

Plan and conduct an investigation to evaluate the transfer of energy or information through different materials by different types of waves such as wireless signals, ultraviolet radiation, and microwaves.

IPC.6.E

Interference and Superposition of Waves

When two waves of the same nature occur in the same region simultaneously, they result in interference. Interference of waves implies that the net effect ...

Reflection of Waves

When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at ...

Reflection and Refraction

Source: Derek Wilson,&#160;Asantha Cooray, PhD, Department of Physics &#38; Astronomy, School of Physical Sciences, University of California, Irvine, CA
...

Interference and Diffraction

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
Interference and diffraction ...

Construct and communicate an evidence-based explanation for how wave interference, reflection, and refraction are used in technology such as medicine, communication, and scientific research.

IPC.6.F

biofuels-producing-ethanol-from-cellulosic-material

Biofuels: Producing Ethanol from Cellulosic Material

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In this experiment, cellulosic material (such as corn stalks, leaves, ...

The Fossil Record

The fossil record documents only a small fraction of all organisms that have ever inhabited Earth. Fossilization is a rare process, and most organisms ...

Nuclear Power

Controlled nuclear fission reactions are used to generate electricity. Any nuclear reactor that produces power via the fission of uranium or plutonium by ...

Sustainable Development

As the human population continues to grow and use resources, we must be mindful of our planet&rsquo;s natural limits. Sustainable development provides a ...

Climate Change

The certainty of climate change remains a public controversy despite the consensus among approximately 97% of active climate researchers, who not only ...

Global Climate Change

Throughout its ~4.5 billion year history, the Earth has experienced periods of warming and cooling. However, the current drastic increase in global ...

Evaluate evidence from multiple sources to critique the advantages and disadvantages of various renewable and nonrenewable energy sources and their impact on society and the environment.

IPC.6.G

Science concepts. The student knows the impact of energy transfer and energy conservation in everyday life. The student is expected to:

Capacitors in Series and Parallel

Description

Transcript

More videos by Standards