Name: circuit parts: branches, nodes, and loops
Uploaded: 2024-04-11T12:48:28.000Z
Duration: 1 min 14 s
Channel: JoVE

Ein elektrisches Netz ist ein System miteinander verbundener Elemente, die nicht unbedingt einen geschlossenen Pfad bilden.
Im Gegensatz dazu muss ein Stromkreis, also auch ein vernetztes System, geschlossene Pfade enthalten.
Während alle Schaltkreise Netzwerke sind, sind nicht alle Netzwerke Schaltkreise.
Basierend auf der Anordnung der Elemente umfasst eine Schaltung Verzweigungen, Knoten, Schleifen und Netze.
Ein Abzweig ist ein Element mit zwei Anschlüssen, z. B. ein Widerstand oder eine Spannungsquelle. Eine Schaltung mit einer Spannungsquelle, einer Stromquelle und zwei Widerständen besteht aus vier Abzweigungen.
Ein Knoten verbindet zwei oder mehr Zweige und wird durch einen Punkt dargestellt. Wenn ein Kurzschluss zwei oder mehr Knoten verbindet, bilden sie einen einzigen Knoten.
Eine Schleife ist ein geschlossener Pfad, der mehrere Knoten durchläuft, ohne einen Knoten zweimal zu überqueren. Wenn die Schleife mindestens einen Zweig hat, der nicht mit anderen Schleifen geteilt wird, ist sie unabhängig.
Ein Netz ist ein Schleifentyp, der keine anderen Schleifen enthält.
Ein Netzwerk, das b Verzweigungen, n Knoten und l unabhängige Schleifen enthält, erfüllt den grundlegenden Satz der Netzwerktopologie.

schaltungsterminologie

Circuit Terminology

Ein elektrisches Netzwerk ist ein System aus miteinander verbundenen Elementen, wie Widerständen, Kondensatoren, Induktoren sowie Spannungs- oder Stromquellen. Im Gegensatz zu einer Schaltung bildet ein elektrisches Netzwerk nicht notwendigerweise einen geschlossenen Pfad. Mit anderen Worten, während alle Schaltungen aufgrund ihrer vernetzten Natur als Netzwerke betrachtet werden können, qualifiziert sich nicht jedes Netzwerk als Schaltung. Eine Schaltung andererseits ist auch ein System aus miteinander verbundenen elektrischen Elementen, muss jedoch einen oder mehrere geschlossene Pfade enthalten. Diese geschlossenen Pfade oder Schleifen ermöglichen einen kontinuierlichen Stromfluss, was den Betrieb der Schaltung ermöglicht. Die Struktur einer Schaltung kann weiter in mehrere Schlüsselkomponenten unterteilt werden: Zweige, Knoten, Schleifen und Maschen. Das Verständnis dieser Komponenten ist entscheidend für die Analyse und das Design von Schaltungen. Ein Zweig stellt ein einzelnes Element der Schaltung dar, wie einen Widerstand, eine Spannungsquelle oder eine Stromquelle, verbunden durch zwei Anschlüsse. Beispielsweise würde eine Schaltung, die eine Spannungsquelle, eine Stromquelle und zwei Widerstände umfasst, aus vier Zweigen bestehen. Knoten sind Punkte in der Schaltung, an denen sich zwei oder mehr Zweige kreuzen. Sie werden in Schaltplänen typischerweise durch einen Punkt dargestellt. Wenn eine Kurzschlussverbindung mehrere Knoten miteinander verbindet, werden sie effektiv zu einem einzigen Knoten. Eine Schleife in einer Schaltung ist ein geschlossener Pfad, der durch mehrere Knoten verläuft, ohne irgendeinen Knoten zweimal zu durchqueren. Schleifen können unabhängig oder abhängig sein. Eine unabhängige Schleife hat mindestens einen Zweig, der nicht mit einer anderen Schleife geteilt wird. Eine Masche andererseits ist eine spezielle Art von Schleife. Es ist ein geschlossener Pfad, der keine anderen Schleifen in sich enthält. Maschen sind grundlegend für bestimmte Arten der Schaltungsanalyse, wie die Maschenanalyse, die systematisch nach Stromwerten löst. Zuletzt werden all diese Elemente durch den fundamentalen Satz der Netzwerk-Topologie zusammengehalten, der besagt, dass für ein Netzwerk mit 'b' Zweigen, 'n' Knoten und 'l' unabhängigen Schleifen diese Mengen durch eine spezifische Formel miteinander verbunden sind, gegeben durch <img alt="Equation1" src="/files/ftp_upload/15067/15067_PT_Equation_1.svg" style="text-align: center; height: 14px;"> Das Verständnis dieser Beziehung ist für die Analyse und den Entwurf elektrischer Netzwerke und Schaltkreise von entscheidender Bedeutung.

Schaltungsterminologie

Ein elektrisches Netz ist ein System miteinander verbundener Elemente, die nicht unbedingt einen geschlossenen Pfad bilden.
Im Gegensatz dazu ist eine Schaltung, auch eine ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Basics of Electric Circuits

Grundlagen elektrischer Stromkreise

KEY TERMS AND CONCEPTS

ZENTRALE BEGRIFFE UND KONZEPTE

circuit parts: branches, nodes, and loops

Circuit parts like branches, nodes, loops, and meshes help describe how electrical networks work. An electrical network is a system of connected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, a network does not have to form a closed path.

A circuit is also made of connected electrical elements, but it must include one or more closed paths. These loops let current flow continuously, which is what makes the circuit operate. Because of this, every circuit is a network, but not every network is a circuit.

A branch is one element of a circuit with two terminals. A resistor, a voltage source, or a current source can each count as a branch. For example, a circuit with one voltage source, one current source, and two resistors has four branches.

Nodes are the points where two or more branches meet. They are usually shown as dots in circuit diagrams. If a short circuit connects several nodes, they act as one node.

A loop is a closed path that passes through several nodes without visiting any node twice. Some loops are independent, which means they have at least one branch not shared with another loop. A mesh is a special loop that contains no other loops inside it.

Meshes are important in mesh analysis, a method used to solve for current values in a circuit. These ideas also connect to the fundamental theorem of network topology. For a network with b branches, n nodes, and l independent loops, these values follow a specific relationship that is important for circuit analysis and design.

Circuit Parts: Branches, Nodes, and Loops

charge and current

Electric Charge in Circuits

Electric charge in circuits explains how charged particles behave in matter and how current is produced. Everyday static effects, like a wool sweater sticking to the body or a shock from a carpet, show charge in action. Charge is an inherent property of atomic particles and is measured in coulombs (C). Matter is made of atoms with electrons, protons, and neutrons. Electrons carry a negative charge (-e), and protons carry a positive charge (+e). These two charges have the same magnitude. An...

voltage

Voltage in Electric Circuits

Voltage in electric circuits is the energy needed to move electric charge between two points. It is also called electromotive force, or EMF. In most circuits, an external force such as a battery provides this energy for electron movement in a conductor. The voltage between points a and b is written as v_ab. It is defined as the work, or energy, needed to move a unit charge from point a to point b. In the equation, w is the energy in joules and q is the charge in coulombs. Voltage is measured...

power and energy

Circuit Power, Absorption, and Supply

Circuit power, absorption, and supply explain how much energy an element uses or delivers in an electric circuit. These ideas matter in electrical engineering because power and energy calculations help describe circuit behavior. A 100-watt light bulb, for example, emits more light than a 60-watt bulb, so wattage is a useful measure in real devices. Power is the time rate of expending or absorbing energy. It is measured in watts, written as W. The relation between power and energy uses the...

electric circuit elements

Circuit Elements: Passive, Active, and Linear

Circuit elements are the building blocks of an electric circuit. An electric circuit is the connection of these elements. In this context, circuit elements are often grouped by how they behave and whether they supply energy. One major group is passive elements. These elements do not generate energy. Common passive elements include resistors, capacitors, and inductors. The other group is active elements, which can generate energy. Generators, batteries, and operational amplifiers are typical...

circuit terminology

Circuit parts like branches, nodes, loops, and meshes help describe how electrical networks work. An electrical network is a system of connected elements, such as resistors, capacitors, inductors, and voltage or current sources. Unlike a circuit, a network does not have to form a closed path. A circuit is also made of connected electrical elements, but it must include one or more closed paths. These loops let current flow continuously, which is what makes the circuit operate. Because of this,...

independent and dependent sources

Circuit Source Symbols and Controls

Circuit sources in electrical circuits can be independent or dependent. They provide the power a circuit needs to operate. Independent voltage sources supply a fixed voltage, and independent current sources supply a fixed current. Their output does not change because of other parts in the circuit. These sources use standard symbols in circuit diagrams. An independent voltage source is shown with + and - signs to mark the potential difference. An independent current source is shown with an...

ohm's law

Resistance and Conductance in Circuits

Resistance and conductance help explain how electric current moves through a circuit. Resistors are basic circuit parts made from metallic alloys or carbon compounds. They are used to model how a material resists current and to control and regulate electrical power in a circuit. Ohm's law describes the link between voltage and current across a resistor. The voltage across a resistor is directly proportional to the current through it. The constant that sets this relationship is resistance.

kirchhoff's current law

Kirchhoff's Current Law at Circuit Nodes

Kirchhoff's Current Law explains how current behaves at a circuit node. A node is the point where two or more circuit elements meet. The law says the current entering a node equals the current leaving it. That balance follows the rule of charge conservation, which means electric charge is not lost at the junction. When applying KCL, currents entering the node are treated as positive and currents leaving the node are treated as negative. The currents can be added algebraically at the node, and...

kirchhoff's voltage law

Voltage Balance in Closed Circuit Loops

Kirchhoff's Voltage Law explains how voltage is balanced in a closed circuit loop. It is a basic rule in electrical engineering and comes from the idea of energy conservation. Energy can change form, but it cannot be created or destroyed. KVL states that the algebraic sum of all voltages around a closed path, or loop, is zero. In other words, the total voltage supplied in a loop equals the total voltage drop across the components in that loop. A loop can be traced clockwise or anticlockwise,...

voltage dividers

Series Resistors and Voltage Split

Series resistors split voltage across a circuit. In a series setup, resistors are linked one after another. The same current flows through each resistor in the chain. To analyze this behavior, Ohm's law is used to relate voltage, current, and resistance. Kirchhoff's voltage law says the voltages around a series loop add up to the source voltage. That means the current in the circuit equals the source voltage divided by the total resistance in series. The current value can then be used in Ohm's...

current dividers

Parallel Resistors and Current Division

Parallel resistors share the same two nodes, so each resistor has the same voltage across it. In this circuit setup, Kirchhoff's current law applies. The source current equals the sum of the currents through each branch. Ohm's law helps find the branch currents from the source voltage and the resistor values. The source current is equal to the source voltage times the sum of the reciprocals of the resistances. This makes it easier to calculate how current divides in the circuit. The current...

equivalent resistance

Delta-Wye Network Conversion

Delta-wye network conversion helps analyze resistor circuits that are not arranged in simple series or parallel paths. These three-terminal equivalent networks use the wye (Y), also called tee (T), and the delta (Δ), also called pi (π), as practical circuit models. These networks are useful in many circuit settings. They appear in three-phase electrical systems, electrical filters, and matching networks. They can also be used on their own or combined with more complex circuits. A delta...

design example: resistive touchscreen

Resistive Touchscreen Voltage Mapping

A resistive touchscreen uses voltage mapping to locate a finger touch on a mobile device. It is built from two metallic layers. The top layer is flexible, and the bottom layer is rigid. A narrow gap separates them, and the high resistance between the layers is an important part of the design. When a user touches the screen, the two layers meet at one point. That contact point is called the touchpoint. The touch lowers the resistance between the layers at that spot and changes the electrical...

key terms and concepts

Learn the key parts of circuits and networks, including branches, nodes, loops, and meshes, plus how these terms support circuit analysis.

Circuit Parts: Branches, Nodes, and Loops | 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

Circuit Parts: Branches, Nodes, and Loops

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