Name: capacitance in series and parallel
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Series and Parallel Capacitors

يمكن توصيل المكثفات في تكوينات متسلسلة و / أو متوازية داخل دائرة.
ضع في اعتبارك المكثفات المتصلة في سلسلة ببطارية ؛ اللوحة المتصلة بالطرف الموجب للبطارية تطور شحنة موجبة ، بينما تصبح اللوحة المتصلة بالطرف السالب سالبة مشحونة.
يتم تحفيز حجم متساو من الشحنة على الألواح الأخرى ، ويتدفق نفس التيار عبر كل مكثف.
يؤدي تطبيق قانون جهد كيرشوف على الحلقة واستبدال الجهد عبر كل مكثف إلى التعبير عن الجهد الكلي عبر المكثف المكافئ ، حيث يساوي الجهد الأولي عبر المكثف المكافئ مجموع الفولتية الأولية عبر كل مكثف.
مقلوب السعة المكافئة هو مجموع المقلوبات للسعات الفردية.
الآن ، إذا كانت المكثفات متصلة بالتوازي ، فإن فرق الجهد المطور عبر كل مكثف يساوي جهد البطارية.
من خلال تطبيق قانون كيرشوف الحالي واستبدال التيار لكل مكثف ، يتم تحديد إجمالي التيار المتدفق عبر المكثف المكافئ. السعة المكافئة هي مجموع السعات الفردية.

المكثفات المتوالية والمتوازية

<div style="direction:rtl">يمكن توصيل المكثفات، وهي مكونات أساسية في الدوائر الإلكترونية، على التوالي و/أو على التوازي. كل تكوين له تأثيرات مختلفة على السلوك العام للدائرة. أولاً، فكر في المكثفات المتصلة على التوالي بالبطارية. في هذا التكوين، تنتج اللوحة المتصلة بالطرف الموجب للبطارية شحنة موجبة، بينما تصبح اللوحة المتصلة بالطرف السالب مشحونة سالبًا. ويتم تحفيز مقدار متساوٍ من الشحنة على الصفائح الأخرى، مما يوضح أن نفس التيار يتدفق عبر كل مكثف في اتصال متسلسل. إن تطبيق قانون كيرشوف للجهد، والذي ينص على أن الجهد الإجمالي حول أي حلقة مغلقة في الدائرة يجب أن يساوي الصفر، على الحلقة واستبدال الجهد عبر كل مكثف ينتج عنه تعبير عن الجهد الإجمالي عبر المكثف المكافئ. في هذه الحالة، الجهد الأولي عبر المكثف المكافئ يساوي مجموع الفولتية الأولية عبر كل مكثف. مقلوب السعة المكافئة في التوصيل المتسلسل هو مجموع مقلوبات السعات الفردية. من ناحية أخرى، عندما يتم توصيل المكثفات على التوازي، فإن فرق الجهد الناتج عبر كل مكثف يساوي جهد البطارية. وذلك لأن جميع المكثفات المتصلة على التوازي تشترك في نفس مصدر الجهد. من خلال تطبيق قانون كيرشوف للتيار، والذي ينص على أن إجمالي التيار الداخل إلى الوصلة يجب أن يساوي إجمالي التيار الخارج منها، واستبدال التيار لكل مكثف، يمكننا تحديد إجمالي التيار المتدفق عبر المكثف المكافئ. في التوصيل الموازي، السعة المكافئة هي ببساطة مجموع السعات الفردية. في الختام، فإن فهم كيفية تصرف المكثفات على التوالي والتكوينات المتوازية أمر بالغ الأهمية في مجال الإلكترونيات. تسمح هذه المعرفة للمهندسين بمعالجة السعة الإجمالية للدائرة، ونتيجة لذلك، التحكم في استجابة الدائرة للإشارات المختلفة. سواء في تطبيقات التصفية، أو تجانس مصدر الطاقة، أو اقتران الإشارة، تلعب المكثفات وتكويناتها دورًا حيويًا.</div>

يمكن توصيل المكثفات في تكوينات متسلسلة و / أو متوازية داخل دائرة.
ضع في اعتبارك المكثفات المتصلة في سلسلة بالبطارية ؛ اللوحة ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Energy Storage Elements

عناصر تخزين الطاقة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الرئيسية

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 charge, which shows that the same current passes through each capacitor in a series path.

Kirchhoff's voltage law is used to analyze the series loop. This law says the total voltage around a closed loop must equal zero. When the capacitor voltages are added, the equivalent capacitor has a total voltage equal to the sum of the individual voltages. For capacitors in series, the reciprocal of the equivalent capacitance equals the sum of the reciprocals of the separate capacitances.

Parallel capacitors behave differently. In a parallel connection, each capacitor has the same potential difference as the battery voltage because they share the same source. Kirchhoff's current law can then be applied at the junction. This law states that current entering a junction must equal current leaving it, which leads to the total current for the equivalent capacitor.

For capacitors in parallel, the equivalent capacitance is the sum of the individual capacitances. Understanding series and parallel capacitor circuits is important in electronics. It helps engineers adjust capacitance for filtering, power supply smoothing, and signal coupling.

Capacitance 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

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 capacitors act in series and parallel circuits, how Kirchhoff's laws apply, and how to calculate equivalent capacitance for high school electronics.

Capacitance in Series and Parallel | 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

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

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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 ...

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

Equivalent Capacitance

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

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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

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Magnetic Fields

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Faraday's Law

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DC Generator

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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 ...

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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 ...

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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

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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

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Velocity and Acceleration of a Wave

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Speed of a Transverse Wave

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Kinetic and Potential Energy of a Wave

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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

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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

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Reflection and Refraction

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

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Biofuels: Producing Ethanol from Cellulosic Material

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
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Sustainable Development

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Climate Change

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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:

Capacitance in Series and Parallel

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