Name: circuit linearity and resistor behavior
Uploaded: 2024-04-11T12:48:31.000Z
Duration: 1 min 17 s
Channel: JoVE

가변 전압 소스에 연결된 저항을 고려하십시오. 전압이 증가하면 해당 전류 값이 기록됩니다.
그래픽 표현은 전압과 전류 사이의 선형 관계를 보여줍니다.
전압 또는 전류의 변화에도 불구하고 회로 매개변수가 일정하게 유지되는 이러한 회로를 선형 회로라고 합니다.
선형 회로는 선형 요소 또는 선형 독립 소스로 구성되며 균질성 및 가산성 속성을 충족합니다.
이 원리는 회로 모델링에서 부하 양단의 전압 강하가 변경될 때 소스 전류를 예측하는 데 도움이 될 수 있습니다.
처음에는 부하 저항을 통과하는 전류와 상단 저항을 통과하는 전압 강하가 결정됩니다.
다음으로, 중앙 분기를 통과하는 전압 강하를 얻어지며, 이는 해당 분기를 통과하는 전류를 계산하는 데 사용됩니다. KCL을 적용하면 총 소스 전류가 제공됩니다.
부하 전압이 변경되면 상수에 이전 전류를 곱하고 알려진 값을 대체하여 새 소스 전류를 찾을 수 있습니다.
그러나 선형성 원리는 전력이 전류에 제곱 의존성을 갖기 때문에 전력 계산에 적용되지 않습니다.

선형 회로

선형 회로는 출력이 입력에 정비례하고 균질성(스케일링) 및 가산성의 원리를 포함하는 선형 특성을 준수하는 것이 특징입니다. 동질성은 여기라고도 하는 입력에 상수 인자를 곱할 때 응답으로 알려진 출력이 그에 따라 동일한 상수 인자에 의해 조정된다는 것을 나타냅니다. 예를 들어, 전류에 상수 'k'를 곱하면 전압도 마찬가지로 'k'배 증가합니다.

가산성 속성은 입력의 합에 대한 응답이 개별적으로 적용된 각 개별 입력에 대한 응답의 합과 동일하다고 규정합니다. 본질적으로 이 속성은 여러 입력이 결합된 경우에도 회로의 동작이 일관되게 유지되도록 합니다.

특히 저항은 전압-전류 관계 내에서 균질성과 가산성 특성을 모두 만족하기 때문에 선형 요소로 분류됩니다. 일반적으로 회로는 가산성과 동질성 특성을 모두 나타내는 경우에만 선형으로 간주됩니다. 이러한 선형 회로는 선형 요소, 선형 종속 소스 및 독립 소스로만 구성됩니다.

반대로, 저항에 대한 전압의 제곱의 비율로 정의되는 전력 표현은 2차 함수를 구성하므로 회로 분석의 맥락에서 비선형성 범주에 속합니다.

가변 전압 소스에 연결된 저항을 고려하십시오. 전압이 증가하면 해당 전류 값이 기록됩니다.
그래픽 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

DC Circuit Analysis

DC 회로 분석

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 equals the sum of the responses to each input applied separately.

A resistor is a linear element because its voltage-current relationship follows both homogeneity and additivity. A circuit is considered linear only when it has both properties. Linear circuits contain linear elements, linear dependent sources, and independent sources.

Power does not follow the same pattern. Its expression uses the square of voltage divided by resistance, so it is a quadratic function. That makes power a nonlinearity in circuit analysis.

Circuit Linearity and Resistor Behavior

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 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...

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 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 circuit linearity depends on homogeneity and additivity, why resistors are linear elements, and why power is treated as nonlinear in circuit analysis.

Circuit Linearity and Resistor Behavior | 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 Linearity and Resistor Behavior

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