Name: mesh currents for circuit analysis
Uploaded: 2024-04-11T12:48:30.000Z
Duration: 1 min 20 s
Channel: JoVE

메시 분석은 메시 전류를 회로 변수로 사용하여 회로 분석과 관련된 동시 방정식의 수를 효과적으로 줄이는 편리한 방법입니다.
노드 해석과 달리 메쉬 해석은 분기를 교차하지 않는 평면 회로에만 적용됩니다.
모든 평면 회로에서 메쉬 전류를 결정하려면 다음 단계가 포함됩니다.
먼저, 회로에 있는 총 독립 메시의 수를 식별하고 메시 전류를 각 메시에 할당합니다.
둘째, 요소 전압은 메쉬 전류의 함수로 표현되며, Kirchhoff의 전압 법칙은 각 메쉬에 적용되어 일련의 선형 방정식을 얻습니다.
마지막으로, 메쉬 전류는 일련의 방정식을 풀어 얻습니다.
"i" 독립 메시가 있는 회로의 경우 메시 해석에는 메시 전류를 얻기 위해 "i" 독립 방정식이 필요합니다.
제시된 2메시 회로에 대한 저항 및 소스 전압 값이 알려져 있다고 가정합니다.
이러한 값은 선형 방정식에 대체되고 메쉬 전류를 얻기 위해 해결됩니다.
마지막으로, 메쉬 전류의 계산된 값을 사용하여 분기 전류 i1, i2 및 i3 을 결정할 수 있습니다.

메쉬 분석

메쉬 분석은 메쉬 전류를 주요 회로 변수로 사용하여 회로 분석을 단순화하는 유용한 방법 중에 하나입니다. 알려지지 않은 전압을 결정하는 데 초점을 맞춘 노드 분석과 달리 메쉬 분석은 키르히호프의 전압 법칙(KVL)을 적용하여 회로 내에서 알려지지 않은 전류를 찾습니다. 이 방법은 풀어야 할 연립 방정식의 수를 줄이는 데 특히 편리합니다.

메쉬 분석의 기본 개념은 메쉬와 메쉬 전류의 정의입니다. 메쉬는 회로 내에 다른 루프가 포함되지 않은 폐쇄 루프입니다. 각 메쉬에는 메쉬 전류가 할당되며 일반적으로 해당 루프 내에서 시계 방향으로 흐르는 것으로 가정을 전재로 합니다

메쉬 분석을 적용하려면 회로가 평면이어야 합니다. 즉, 가지가 서로 교차하지 않고 평평한 표면에 그릴 수 있어야 합니다. 평면 회로는 프로세스를 단순화하므로 메쉬 분석에 이상적입니다. 메쉬 분석과 관련된 단계는 다음과 같습니다.

<ul style="list-style-type: disc; display: flex; flex-direction: column; gap: 10px; padding: 0 0 0 40px;">
	<li>회로의 "n"개의 독립 메쉬 각각에 메쉬 전류를 할당합니다.</li>
	<li>각 "n" 메쉬에 KVL을 적용하여 옴의 법칙을 사용하여 메쉬 전류로 요소 전압을 표현합니다.</li>
	<li>결과 "n" 연립 방정식을 풀어 메쉬 전류 값을 얻습니다.</li>
</ul>

이러한 메쉬 전류는 회로 내의 다양한 분기 전류를 결정할 수 있습니다. 메쉬가 분리되지 않는 한 메쉬 전류는 분기 전류와 구별된다는 점에 유의하는 것이 중요합니다.

메쉬 해석은 메쉬 전류를 회로 변수로 사용하여 관련된 동시 방정식의 수를 효과적으로 줄이는 편리한 방법입니다.

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

DC Circuit Analysis

DC 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Mesh Analysis

mesh currents for circuit analysis

Mesh currents give students a simpler way to analyze planar circuits. In mesh analysis, the unknowns are currents, not voltages. The method uses Kirchhoff's voltage law, or KVL, to build the equations needed to solve the circuit.

A mesh is a closed loop in a circuit that does not contain any smaller loops inside it. Each independent mesh is assigned a mesh current, and this current is usually drawn in the clockwise direction. These mesh currents are used as the main circuit variables during analysis.

Mesh analysis works only for planar circuits. A planar circuit is one that can be drawn on a flat surface without any branches crossing. This shape makes the method easier to apply because the loops are clear and separate.

The process starts by assigning mesh currents to the n independent meshes in the circuit. Next, KVL is applied to each mesh, and element voltages are written in terms of mesh currents using Ohm's law. The resulting n simultaneous equations are then solved to find the mesh currents, which can be used to determine branch currents. Mesh currents and branch currents are not the same unless a mesh is isolated.

Mesh Currents for Circuit Analysis

nodal analysis

Using Node Voltages in Circuit Analysis

Nodal analysis uses node voltages to simplify circuit analysis. In this method, the voltage at each node becomes the main variable. Once those voltages are known, they can be used to find other values, such as the current through specific circuit parts. The process begins by choosing a reference node, also called a datum node. This node is selected for convenience and assigned a voltage of zero. The other nodes, called non-reference nodes, are then measured relative to that point. In the...

nodal analysis with voltage sources

Supernode Equations in Nodal Analysis

Nodal analysis uses node voltages and Kirchhoff’s laws to solve circuits with voltage sources. It is a systematic method for breaking a complex circuit into smaller parts that are easier to analyze. In this example, the circuit includes four resistors and two voltage sources. One voltage source is connected between a non-reference node and the reference node. In that case, the non-reference node voltage can be written directly as the source voltage. This removes one unknown and makes the...

mesh analysis

Mesh currents give students a simpler way to analyze planar circuits. In mesh analysis, the unknowns are currents, not voltages. The method uses Kirchhoff's voltage law, or KVL, to build the equations needed to solve the circuit. A mesh is a closed loop in a circuit that does not contain any smaller loops inside it. Each independent mesh is assigned a mesh current, and this current is usually drawn in the clockwise direction. These mesh currents are used as the main circuit variables during...

mesh analysis with current sources

Current Sources in Mesh Circuit Analysis

Current sources make mesh circuit analysis easier because they can reduce the number of equations needed. This applies to both independent and dependent current sources. The method depends on where the current source is placed in the circuit. When a current source appears in only one mesh, the setup is simple. Assign mesh currents as usual, but leave out the mesh that contains the current source from the equation process. Then apply Kirchhoff's voltage law, or KVL, to the remaining mesh to get...

source transformation

Circuit Source Equivalents

Circuit source equivalents make it easier to simplify electrical circuits in circuit analysis. A source transformation replaces a voltage source in series with a resistor by a current source in parallel with a resistor, or it replaces a current source in parallel with a resistor by a voltage source in series with a resistor. The key idea is that the equivalent resistance at the circuit terminals stays the same when the original sources are turned off. When making the change, the current source...

linear circuits

Circuit Linearity and Resistor Behavior

Circuit linearity describes how a circuit responds when its input changes. A linear circuit has an output that is directly proportional to its input. This behavior follows two rules: homogeneity and additivity. Homogeneity means that if the input, or excitation, is multiplied by a constant factor, the response is multiplied by the same factor. For example, if the current is increased by a constant k, the voltage also increases by k times. Additivity means that the response to a sum of inputs...

superposition theorem

Analyzing Circuits with Superposition

Superposition is a circuit analysis method for linear circuits with more than one independent source. It lets you find the voltage across or current through an element by adding the separate effects of each source acting alone. To use superposition, keep one independent source active and turn off the others. A voltage source is replaced by a short circuit, and a current source is replaced by an open circuit. Then calculate the output from the single active source. Repeat the process for each...

thevinin's theorem

Thevenin Circuit Equivalents

Thevenin circuit equivalents simplify linear two-terminal circuits by replacing the fixed part of a network with one equivalent source and one resistor. This method is useful when a circuit has a fixed section and a load that can change. A household electrical outlet is a familiar example, because different appliances can be plugged in or removed. Each change in load can require a new circuit analysis, so an equivalent circuit makes the work easier. Thevenin's theorem states that a linear...

norton's theorem

Norton Equivalent Circuit in DC Analysis

Norton equivalent circuit in DC analysis shows how a linear two-terminal circuit can be replaced by a simpler network. The replacement uses a current source, called I_N, in parallel with a resistor, called R_N. I_N is the short-circuit current through the terminals, and R_N is the input or equivalent resistance seen at the terminals when the independent sources are turned off. To find Norton's resistance, all independent sources in the circuit are set to zero. The resistance measured at the...

maximum power transfer

Load Matching in Thevenin Circuits

Load matching in Thevenin circuits helps a source deliver the most power to a connected load. This matters in engineering fields such as telecommunications, where power delivery must be optimized. Even then, internal losses can be significant and may equal or exceed the power sent to the load. The Thevenin equivalent circuit is a useful way to study this situation. It replaces the full linear circuit with a simpler source and resistance while keeping the load in place. In this setup, the load...

design example: strain gauge bridge or wheatstone bridge

design-example-strain-gauge-bridge-or-wheatstone-bridge

Wheatstone Bridge Output for Strain Gauge Design

A strain gauge and Wheatstone bridge work together to turn mechanical strain into an electrical signal. In engineering, this setup is often used to measure force or pressure. Each part of the bridge has a resistance that changes slightly when strain is applied. The main goal is to turn a very small voltage output into a larger, easier-to-read signal. A voltmeter can then measure that output more clearly. To do this, an engineer designs the strain gauge circuit and figures out how much...

key terms and concepts

Learn how mesh currents and Kirchhoff's voltage law simplify planar circuit analysis by turning loops into solvable current equations for high school students.

Mesh Currents for Circuit Analysis | 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

Mesh Currents for Circuit Analysis

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