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

Consider a resistor connected to a variable voltage source. As the voltage is increased, the corresponding current value is recorded.
The graphical representation reveals a linear relationship between the voltage and current.
Such circuits where circuit parameters remain consistent despite changes in voltage or current are called linear circuits.
Linear circuits are composed of linear elements or linear independent sources, and they satisfy homogeneity and additivity properties.
This principle can help in circuit modeling to predict the source current when the voltage drop across the load changes.
Initially, the current through the load resistor and the voltage drop across the top resistor are determined.
Next, the voltage drop across the central branch is obtained, which is used to calculate the current through that branch. Applying KCL gives the total source current.
When the load voltage changes, the new source current can be found by multiplying a constant with the old current and substituting the known values.
However, the linearity principle does not apply to the power calculation, as power has a square dependence on the current.

linear circuits

A linear circuit is characterized by its output having a direct proportionality to its input, adhering to the linearity property, which encompasses the principles of homogeneity (scaling) and additivity. Homogeneity dictates that when the input, also referred to as the excitation, is multiplied by a constant factor, the output, known as the response, is correspondingly scaled by the same constant factor. For instance, if the current is multiplied by a constant &#39;k,&#39; the voltage likewise experiences an increase of &#39;k&#39; times.
The additivity property stipulates that the response to a sum of inputs equals the sum of responses to each individual input applied separately. In essence, this property enforces that the circuit&#39;s behavior remains consistent even when multiple inputs are combined.
Notably, a resistor is classified as a linear element because it satisfies both the homogeneity and additivity properties within its voltage-current relationship. Generally, a circuit is considered linear if and only if it demonstrates both additivity and homogeneity characteristics. Such linear circuits exclusively comprise linear elements, linear dependent sources, and independent sources.
Conversely, the expression for power, which is defined as the ratio of the square of voltage to resistance, constitutes a quadratic function and, therefore, falls under the category of nonlinearity within the context of circuit analysis.

Linear Circuits

Consider a resistor connected to a variable voltage source. As the voltage is increased, the corresponding current value is recorded.
The graphical ...

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JoVE Core

Electrical Engineering

Unit 1

DC Circuit Analysis

KEY TERMS AND CONCEPTS

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

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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

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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...

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...

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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

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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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