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

电路网络是由相互连接的元件组成的系统，这些元件不一定形成闭合路径。
相比之下，电路也是一种相互连接的系统，但必须包含闭合路径。
虽然所有电路都是网络，但并非所有网络都是电路。
根据元件的排列方式，电路包含支路、节点、回路和网孔。
支路是一种双端元件，例如电阻器或电压源。一个包含电压源、电流源和两个电阻器的电路由四条支路组成。
节点连接两个或更多支路，用一个点表示。如果短路连接了两个或更多节点，则它们构成单个节点。
回路是一条闭合路径，它经过多个节点但不会重复经过任一节点。如果该回路至少包含一条不与其他回路共享的支路，则该回路是独立的。
网孔是一种不包含其他回路的回路类型。
一个包含 b 条支路、n 个节点和 l 个独立回路的网络满足网络拓扑的基本定理。

电路术语

Circuit Terminology

电气网络是由互连元件（例如电阻器、电容器、电感器以及电压或电流源）所组成的系统。与电路不同的是，电网不一定会形成闭合的路径。换句话说，虽然所有电路由于其互连性质都可以被视为网络，但并非每个网络都有资格作为电路。 另一方面，电路也是电气元件中的互连系统，但必须包含一个或多个闭合路径。这些闭合路径或环路允许电流进行连续的流动，从而使得维持电路的运行成为可能。 电路的结构可以进一步分解为几个关键的部分：分支、节点、环路和网格。了解这些组件对于分析和设计电路是至关重要的。 分支代表了电路中的单个元件，例如通过两个端子所连接的电阻器、电压源或电流源。例如，包含电压源、电流源和两个电阻器的电路将会由四个分支组成。 节点是由电路中两个或多个分支相交的点所组成。它们通常在电路图中用点来进行表示。如果短路能够将多个节点连接在一起，则它们实际上就变成了单个节点。 电路中的环路是经过多个节点而不经过任何两次闭合的节点路径。循环可以是独立的，也可以是相关的。但是独立循环至少有一个不与任何其他循环共享的分支。 另一方面，网格是一种特殊类型的循环。它是一条闭合路径，其中不包含任何的其他循环。网格对于某些类型的电路分析是至关重要的，例如网格分析，它能够系统地对电流值进行求解。 最后，所有这些元素都能够通过网络拓扑的基本定理联系在一起，该定理指出，对于包含“b”个分支、“n”个节点和“l”个独立环路的网络，这些量由一个特定的公式联系在一起: <img alt="Equation1" src="/files/ftp_upload/15067/15067_PT_Equation_1.svg" style="text-align: center; height: 14px;"> 理解这种关系对于电气网络和电路的分析和设计是至关重要的。

一个电路网络是由相互连接的元件组成的系统，这些元件不一定形成闭合回路。  
相比之下，电路也是一种相互连接的……

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Basics of Electric Circuits

电路基础

KEY TERMS AND CONCEPTS

关键术语与概念

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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