Engineering · Electrical engineering/Control

Thevenin equivalent of a linear two-terminal network

A linear network viewed at two terminals can be replaced by an ideal voltage source in series with a resistance.

AdvancedUniversity/collegeBachelor foundationsSubject specialization

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Formula

U_{T h} = U_{oc}, R_{T h} = \frac{U _{oc}}{I _{sc}}

U in V; I in A; R in Ω

Variables & units

Variables & units
Symbol	Meaning	Unit
$UTh$	Open-circuit terminal voltage	V
$RTh$	Equivalent internal resistance	Ω
$Isc$	Short-circuit current at the same terminals	A

LaTeX

U_{Th}=U_{oc},\quad R_{Th}=\frac{U_{oc}}{I_{sc}}

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Derivation & background

The equivalent reproduces the terminal behavior of a linear network for attached loads. UTh is the open-circuit voltage; RTh can be found with independent sources deactivated or from Uoc/Isc. Dependent sources remain active and need separate treatment. Nonlinear elements generally have no global Thevenin pair.

Exam blueprint

Validity range

Derivation steps

A linear network viewed at two terminals can be replaced by an ideal voltage source in series with a resistance.

1State the model assumptions and list quantities with units.
2Substitute into UTh = Uoc; RTh = Uoc/Isc; convert quantities to SI first.
3A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V.

Rearrangements

Base equation for the target quantity

U_{Th}=U_{oc},\quad R_{Th}=\frac{U_{oc}}{I_{sc}}

Preserve signs, boundary conditions and units when rearranging.

Task variant

Work through the numerical example for “Thevenin equivalent of a linear two-terminal network” and check its unit and magnitude.

A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V.

Common mistakes

Substituting a related quantity that shares the same symbol.

Use variable definitions and check: U in V; I in A; R in Ω.

Exam context

Reduce a complex linear circuit when analyzing one load.

Formula cluster

Electrical engineering/Control

A linear network viewed at two terminals can be replaced by an ideal voltage source in series with a resistance.

Uout = Uin·R₂/(R₁+R₂)

Voltage divider with two series resistors

U = R·I

Ohm's Law

Σ I hinein = Σ I hinaus; Σ ΔV = 0

Kirchhoff’s junction and loop rules

Worked example

A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V.

Applications

Reduce a complex linear circuit when analyzing one load.

How do you calculate with Thevenin equivalent of a linear two-terminal network?

Here is how to work through a typical Thevenin equivalent of a linear two-terminal network (UTh = Uoc; RTh = Uoc/Isc) task step by step:

1
Task
Work through the numerical example for “Thevenin equivalent of a linear two-terminal network” and check its unit and magnitude.
Solution path
A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V.

Frequently asked questions about Thevenin equivalent of a linear two-terminal network

How do I find UTh?+

Remove the load at the chosen terminals and calculate the open-circuit voltage with consistent polarity. That voltage is UTh. Keep dependent sources active; a test source may be needed to find resistance. Keep terminals and source convention fixed; retain dependent sources while finding resistance. Application: Reduce a complex linear circuit when analyzing one load. The numerical example A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V anchors the idea in a concrete measurement case.

How do I determine RTh?+

For a linear network with independent sources, short ideal voltage sources and open ideal current sources, then look into the terminals. Alternatively use RTh=Uoc/Isc when both are measured consistently. Do not deactivate dependent sources. Keep terminals and source convention fixed; retain dependent sources while finding resistance. The corresponding units are U in V; I in A; R in Ω. A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V. This checks that the reference quantities are compatible.

For which loads does the equivalent apply?+

A correct Thevenin model reproduces terminal voltage-current behavior for any attached load while the surrounding network remains linear. It does not preserve internal voltages or powers. Time-varying or nonlinear sources require an adapted model. Keep terminals and source convention fixed; retain dependent sources while finding resistance. Scope: The equivalent reproduces the terminal behavior of a linear network for attached loads. UTh is the open-circuit voltage; RTh can be found with independent sources deactivated or from Uoc/Isc. Dependent sources remain active and need separate treatment. Nonlinear elements generally have no global Thevenin pair. A practical application is Reduce a complex linear circuit when analyzing one load.

How do I check the result and units for Thevenin equivalent of a linear two-terminal network?+

Write the quantity and unit from the variable list next to every value: U in V; I in A; R in Ω. Substitute only after converting to a consistent unit system, and state sign or reference direction explicitly. The example A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V. is a calculation check: result, unit and order of magnitude must fit the described situation. Round after intermediate calculations so small contributions are not lost prematurely. Keep terminals and source convention fixed; retain dependent sources while finding resistance.

Which model limit matters for Thevenin equivalent of a linear two-terminal network?+

The background states this starting condition: The equivalent reproduces the terminal behavior of a linear network for attached loads. UTh is the open-circuit voltage;. That limits when the result is a valid model prediction. Compare the problem’s boundary conditions with this assumption before substituting values; real components, material properties or loads can introduce additional effects. The cited reference supports the relation used here but does not remove the need to check whether the specific case fits the model. Keep terminals and source convention fixed; retain dependent sources while finding resistance.

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Subject references and further reading

This list names subject references and further reading. A page or section number appears when it is part of the reference; these are not verbatim quotations.

[1]MIT OpenCourseWare, Circuits and Electronics, Thevenin equivalent circuit notes.

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Thevenin equivalent of a linear two-terminal network

A linear network viewed at two terminals can be replaced by an ideal voltage source in series with a resistance.

AdvancedUniversity/collegeBachelor foundationsSubject specialization

Free to browse · flashcards or a multiple-choice quiz · import from Essential

Symbol

Meaning

Unit

UTh

Open-circuit terminal voltage

RTh

Equivalent internal resistance

Isc

Short-circuit current at the same terminals

Derivation & background

Exam blueprint

Validity range

Derivation steps

A linear network viewed at two terminals can be replaced by an ideal voltage source in series with a resistance.

1State the model assumptions and list quantities with units.
2Substitute into UTh = Uoc; RTh = Uoc/Isc; convert quantities to SI first.
3A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V.

How do you calculate with Thevenin equivalent of a linear two-terminal network?

Here is how to work through a typical Thevenin equivalent of a linear two-terminal network (UTh = Uoc; RTh = Uoc/Isc) task step by step:

Task

Work through the numerical example for “Thevenin equivalent of a linear two-terminal network” and check its unit and magnitude.

Solution path

A network with Uoc=12 V and Isc=2 A has RTh=6 Ω; a 6 Ω load receives 6 V.

Frequently asked questions about Thevenin equivalent of a linear two-terminal network

How do I find UTh?+

How do I determine RTh?+

For which loads does the equivalent apply?+

How do I check the result and units for Thevenin equivalent of a linear two-terminal network?+

Which model limit matters for Thevenin equivalent of a linear two-terminal network?+

Retain Thevenin equivalent of a linear two-terminal network for exams

Create a curated FSRS exam set for UTh = Uoc; RTh = Uoc/Isc: formula recall, variables, derivation, rearrangement, worked example, common mistakes and exam context.

Curated formula set · LaTeX · FSRS spaced repetition · import from Essential