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

Considérons une résistance connectée à une source de tension variable. Lorsque la tension augmente, la valeur de courant correspondante est enregistrée.
La représentation graphique révèle une relation linéaire entre la tension et le courant.
De tels circuits où les paramètres du circuit restent cohérents malgré les changements de tension ou de courant sont appelés circuits linéaires.
Les circuits linéaires sont composés d’éléments linéaires ou de sources linéaires indépendantes, et ils satisfont aux propriétés d’homogénéité et d’additivité.
Ce principe peut aider à la modélisation des circuits pour prédire le courant source lorsque la chute de tension aux bornes de la charge change.
Initialement, le courant traversant la résistance de charge et la chute de tension aux bornes de la résistance supérieure sont déterminés.
Ensuite, la chute de tension aux bornes de la branche centrale est obtenue, qui est utilisée pour calculer le courant à travers cette branche. L’application de KCL donne le courant source total.
Lorsque la tension de charge change, le nouveau courant source peut être trouvé en multipliant une constante par l’ancien courant et en substituant les valeurs connues.
Cependant, le principe de linéarité ne s’applique pas au calcul de la puissance, car la puissance dépend carrément du courant.

circuits linéaires

Un circuit linéaire se caractérise par sa sortie ayant une proportionnalité directe à son entrée, adhérant à la propriété de linéarité, qui englobe les principes d'homogénéité (mise à l'échelle) et d'additivité. L'homogénéité signifie que lorsque l'entrée, également appelée excitation, est multipliée par un facteur constant, la sortie, appelée réponse, est mise à l'échelle en conséquence par le même facteur constant. Par exemple, si le courant est multiplié par un « k » constant, la tension subit également une augmentation de « k » fois. La propriété d'additivité stipule que la réponse à une somme d'entrées est égale à la somme des réponses à chaque entrée individuelle appliquée séparément. Essentiellement, cette propriété garantit que le comportement du circuit reste cohérent même lorsque plusieurs entrées sont combinées. Notamment, une résistance est classée comme élément linéaire car elle satisfait à la fois aux propriétés d’homogénéité et d’additivité dans sa relation tension-courant. Généralement, un circuit est considéré comme linéaire si et seulement s'il présente à la fois des caractéristiques d'additivité et d'homogénéité. De tels circuits linéaires comprennent exclusivement des éléments linéaires, des sources linéaires dépendantes et des sources indépendantes. À l’inverse, l’expression de la puissance, qui est définie comme le rapport du carré de la tension à la résistance, constitue une fonction quadratique et relève donc de la catégorie de non-linéarité dans le contexte de l’analyse des circuits.

Circuits linéaires

Considérons une résistance connectée à une source de tension variable. Lorsque la tension augmente, la valeur de courant correspondante est enregistrée.
Le graphique ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

DC Circuit Analysis

Analyse des circuits CC

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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

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mesh analysis

Mesh Currents for Circuit Analysis

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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

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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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