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

ניתן לחבר קבלים בתצורות סדרתיות ו/או מקביליות בתוך מעגל.
חשבו על הקבלים המחוברים בסדרה לסוללה; הלוחית המחוברת למסוף החיובי של הסוללה מפתחת מטען חיובי, בעוד שהלוחית המחוברת למסוף השלילי הופכת לבעלת מטען שלילי.
גודל שווה של המטען מושרה על הלוחות האחרים, ואותו זרם זורם דרך כל קבל.
החלת חוק המתח של קירכהוף על הלולאה והחלפת המתח על פני כל קבל מניבה את הביטוי למתח הכולל על פני הקבל המקביל, כאשר המתח ההתחלתי על פני הקבל המקביל שווה לסכום המתחים ההתחלתיים על פני כל קבל.
הגומלין של הקיבול המקביל הוא סכום ההדדיות של הקיבולים הבודדים.
כעת, אם הקבלים מחוברים במקביל, הפרש הפוטנציאלים שנוצר על פני כל קבל שווה למתח הסוללה.
על ידי החלת החוק הנוכחי של קירכהוף והחלפת הזרם עבור כל קבל, נקבע הזרם הכולל הזורם דרך הקבל המקביל. הקיבול המקביל הוא סכום הקיבולים הבודדים.

קבלים סדרתיים ומקבילים

<div style="direction:rtl">קבלים, רכיבים בסיסיים במעגלים אלקטרוניים, יכולים להיות מחוברים בתצורות סדרתיות ו/או מקבילות. לכל תצורה יש השפעות שונות על ההתנהגות הכוללת של המעגל. ראשית, שקול קבלים המחוברים בסדרה לסוללה. בתצורה זו, הלוח המחובר למסוף החיובי של הסוללה מפתח מטען חיובי, בעוד שהלוח המחובר למסוף השלילי הופך לטעון שלילי. גודל שווה של מטען מושרה על הלוחות האחרים, מה שממחיש שאותו זרם זורם דרך כל קבל בחיבור סדרתי. החלת חוק המתח של קירכהוף, הקובע שהמתח הכולל סביב כל לולאה סגורה במעגל חייב להיות שווה לאפס, על הלולאה והחלפת המתח על פני כל קבל מניב ביטוי למתח הכולל על פני הקבל המקביל. במקרה זה, המתח ההתחלתי על פני הקבל השקול שווה לסכום המתחים ההתחלתיים על פני כל קבל. ההדדיות של הקיבול השקול בחיבור סדרתי הוא סכום ההדדיות של הקיבולים הבודדים. מצד שני, כאשר קבלים מחוברים במקביל, הפרש הפוטנציאלים שפותח על פני כל קבל שווה למתח הסוללה. הסיבה לכך היא שכל הקבלים בתצורה מקבילה חולקים את אותו מקור מתח. על ידי יישום החוק הנוכחי של קירכהוף, הקובע שסך הזרם הנכנס לצומת חייב להיות שווה לזרם הכולל היוצא ממנו, והחלפת הזרם בכל קבל, נוכל לקבוע את סך הזרם הזורם דרך הקבל השקול. בחיבור מקבילי, הקיבול השקול הוא פשוט סכום הקיבולים הבודדים. לסיכום, הבנת האופן שבו קבלים מתנהגים בתצורות סדרתיות ומקבילות היא חיונית באלקטרוניקה. ידע זה מאפשר למהנדסים לתפעל את הקיבול הכולל של מעגל וכתוצאה מכך לשלוט בתגובת המעגל לאותות שונים. בין אם ביישומי סינון, החלקת אספקת חשמל או צימוד אותות, הקבלים והתצורות שלהם ממלאים תפקיד חיוני.</div>

ניתן לחבר קבלים בתצורות סדרתיות ו/או מקביליות בתוך מעגל.
שקול את הקבלים המחוברים בסדרה לסוללה; הצלחת. . .

Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

Energy Storage Elements

רכיבי אגירת אנרגיה

KEY TERMS AND CONCEPTS

מונחי מפתח ומושגי יסוד

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...

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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...

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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

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By integrating the equation relating voltage and ...

Capacitors can be connected in series and/or parallel configurations within a circuit.
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Equivalent Capacitance

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Inductors

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IPC.6.B

Energy

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Conservation of Energy

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IPC.6.C

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IPC.6.D

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IPC.6.E

Interference and Superposition of Waves

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IPC.6.F

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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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