---
title: "Norton Equivalent | Electrical Circuits and Systems II"
description: "Norton Equivalent is a circuit model that replaces a linear network with a current source in parallel with a resistor, simplifying load analysis in Circuits II."
canonical: "https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-equivalent"
type: "key-term"
subject: "Electrical Circuits and Systems II"
unit: "Unit 7"
---

# Norton Equivalent | Electrical Circuits and Systems II

## Definition

A Norton equivalent is a linear circuit rewritten as a current source in parallel with a resistance seen at the output terminals. In Electrical Circuits and Systems II, it makes load and two-port analysis much easier.

## What It Is

A Norton equivalent is the current-source version of a simplified circuit model in Electrical Circuits and Systems II. Instead of carrying around a complicated network, you replace everything at a pair of terminals with one current source in parallel with one resistor. That pair behaves the same way as the original circuit as far as the outside load is concerned.

The two Norton values are the short-circuit current, called $I_N$, and the equivalent resistance, $R_N$. $I_N$ is the current that flows if you short the output terminals together. $R_N$ is the resistance you see looking back into the network after independent sources are turned off, which means voltage sources become shorts and current sources become opens.

That second step is where a lot of students get tripped up. You are not finding the resistance of every part in the circuit by itself. You are finding the input resistance seen from the terminals after removing the effect of the independent sources. If dependent sources are present, you usually cannot just switch them off, so you may need a test source or another method to find the resistance correctly.

The Norton form is one of the two classic terminal equivalents, along with the Thévenin equivalent. They are directly related: the same network can be written as either form, and the resistance is the same in both. The current source and resistor in the Norton model are just a different way to package the same terminal behavior.

A compact way to think about it is this: Thévenin is a voltage source in series with a resistor, while Norton is a current source in parallel with a resistor. If you know one form, you can convert to the other and choose the version that makes the next calculation cleaner. For circuits with parallel loads or current-focused analysis, Norton often feels more natural.

## Why It Matters

Norton equivalent shows up anywhere you need to simplify a linear circuit before checking what a load will actually get. In this course, that usually means reducing a complicated source network, amplifier stage, or transformer-related circuit to a clean terminal model so you can solve for load current without redoing the full circuit each time.

It also gives you a fast way to compare different circuits by their output behavior. Two networks can look totally different internally, but if they have the same Norton equivalent, they deliver the same current to anything attached at the terminals. That is a big deal in two-port network work, where you often care less about every internal branch and more about how one side of the circuit responds to the other.

For non-ideal transformer models, Norton form helps when winding resistance, leakage effects, or reflected impedances make the circuit messy. Converting to a Norton model can make current division and load-current calculations much cleaner than trying to work through the whole transformer network each time.

It also reinforces a core Circuits II skill: reading a circuit from the terminals inward. That is the mindset behind black-box modeling, impedance matching, and many equivalent-circuit problems. If you can find the Norton form correctly, you are also showing that you know how sources, resistors, and dependent elements behave under circuit simplification.

## Connections

### [Thevenin Equivalent](/electrical-circuits-systems-ii/key-terms/thevenin-equivalent)

Thevenin and Norton are two ways to describe the same linear network at its terminals. Thevenin uses a voltage source in series with a resistance, while Norton uses a current source in parallel with the same resistance. If a problem asks for load voltage, Thevenin can feel more direct. If it asks for load current or parallel combinations, Norton is often easier to use.

### Dependent Source

Dependent sources change how you find the Norton resistance. You usually cannot turn them off the same way you do independent sources, because their values depend on circuit variables. That means a simple source-killing step may not be enough, and you may need a test source or another terminal-analysis method to get the correct equivalent resistance.

### Two-Port Network

A Norton equivalent is a terminal model, which fits naturally with two-port thinking. In two-port analysis, you care about how input and output variables relate, not every internal component. Norton form gives a compact current-based way to describe one side of a network when you are building or reducing a black-box representation.

### [Impedance Matching](/electrical-circuits-systems-ii/key-terms/impedance-matching)

Impedance matching is easier to reason about once a circuit has been reduced to a Norton or Thévenin form. The equivalent resistance tells you how the source network interacts with the load, so you can predict current transfer and power transfer. In many problems, the Norton form makes the load-current side of matching feel more direct.

## On the AP Exam

A problem set or quiz item will usually ask you to find the Norton equivalent seen by a load and then use it to calculate the load current. The move is to identify the output terminals, short them to get $I_N$, and then find $R_N$ by turning off independent sources or by using a test source if dependent sources are present. After that, you redraw the circuit as a current source in parallel with $R_N$ and combine it with the load.

You may also be asked to convert between Norton and Thévenin forms. In that case, use $I_N = V_{th}/R_{th}$ and keep the resistance the same. If the circuit includes a non-ideal transformer or a two-port network, the cleaner answer often comes from reducing one side to a Norton model first and then solving the current relationships at the terminals.

## Norton Equivalent vs Thevenin Equivalent

These two are the same network expressed in different forms, so they are easy to mix up. Norton uses a current source in parallel with a resistor, while Thevenin uses a voltage source in series with a resistor. The resistance value is the same in both models, but the source quantity changes based on whether you are looking at current or voltage behavior.

## Key Takeaways

- A Norton equivalent replaces a linear circuit with a current source in parallel with a resistance at the output terminals.
- The Norton current is found from the short-circuit current, and the Norton resistance is the resistance seen looking into the terminals.
- Independent voltage sources are shorted and independent current sources are opened when you find the equivalent resistance.
- Norton and Thevenin are equivalent descriptions of the same terminal behavior, so you can convert between them when a problem is easier in one form.
- This model is especially useful in load-current problems, two-port networks, and non-ideal transformer circuits.

## FAQs

### What is Norton Equivalent in Electrical Circuits and Systems II?

A Norton equivalent is a simplified terminal model for a linear circuit, made of a current source in parallel with a resistor. It represents the same behavior seen by a load connected to the circuit terminals. In Circuits II, you use it to reduce a messy network before solving for current.

### How do you find the Norton equivalent?

First, short the output terminals and calculate the short-circuit current, which becomes $I_N$. Then find the resistance seen from the terminals with independent sources turned off, which gives $R_N$. If dependent sources are present, you may need a test source instead of just turning sources off.

### What is the difference between Norton and Thevenin equivalents?

They describe the same circuit from the same terminals, but in different forms. Norton uses a current source in parallel with a resistor, while Thevenin uses a voltage source in series with a resistor. You can convert between them using $I_N = V_{th} / R_{th}$.

### Why do dependent sources make Norton resistance harder to find?

Because dependent sources are controlled by circuit variables, not independent source labels, so you usually cannot just turn them off. If you do, you change the circuit behavior incorrectly. A test source method is often the safer way to find the correct terminal resistance.

## Related Study Guides

- [7.3 Non-ideal transformer characteristics and equivalent circuits](/electrical-circuits-systems-ii/unit-7/non-ideal-transformer-characteristics-equivalent-circuits/study-guide/LtkPYr8pD30StXQo)
- [11.1 Two-port network representations](/electrical-circuits-systems-ii/unit-11/two-port-network-representations/study-guide/iGxWy97eJ5DmIKap)

## About This Document

Canonical Fiveable pages are available as Markdown at the same path plus `.md`.

- [llms.txt](https://fiveable.me/llms.txt): index of Fiveable's sections and URL patterns
- [llms-full.txt](https://fiveable.me/llms-full.txt): complete subject and unit listing
- [MCP server](https://fiveable.me/mcp): call Fiveable as tools instead of fetching pages (`https://fiveable.me/api/mcp`)
- [MCP server for AP teachers](https://fiveable.me/mcp/teachers): a teacher's classes, assignments and AP-rubric grading (`https://fiveable.me/api/mcp/teacher`)

## Structured Data

```json
{"@context":"https://schema.org","@graph":[{"@type":"LearningResource","@id":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-equivalent#resource","name":"Norton Equivalent | Electrical Circuits and Systems II","url":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-equivalent","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-equivalent#term"},"audience":{"@type":"EducationalAudience","educationalRole":"student"},"dateModified":"2026-07-03T02:21:24.034Z","isPartOf":{"@type":"Collection","name":"Electrical Circuits and Systems II Key Terms","url":"https://fiveable.me/electrical-circuits-systems-ii/key-terms"},"publisher":{"@type":"Organization","name":"Fiveable","url":"https://fiveable.me"}},{"@type":"DefinedTerm","@id":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-equivalent#term","name":"Norton Equivalent","description":"A Norton equivalent is a linear circuit rewritten as a current source in parallel with a resistance seen at the output terminals. In Electrical Circuits and Systems II, it makes load and two-port analysis much easier.","url":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-equivalent","inDefinedTermSet":{"@type":"DefinedTermSet","name":"Electrical Circuits and Systems II Key Terms","url":"https://fiveable.me/electrical-circuits-systems-ii/key-terms"}},{"@type":"FAQPage","mainEntity":[{"@type":"Question","name":"What is Norton Equivalent in Electrical Circuits and Systems II?","acceptedAnswer":{"@type":"Answer","text":"A Norton equivalent is a simplified terminal model for a linear circuit, made of a current source in parallel with a resistor. It represents the same behavior seen by a load connected to the circuit terminals. In Circuits II, you use it to reduce a messy network before solving for current."}},{"@type":"Question","name":"How do you find the Norton equivalent?","acceptedAnswer":{"@type":"Answer","text":"First, short the output terminals and calculate the short-circuit current, which becomes $I_N$. Then find the resistance seen from the terminals with independent sources turned off, which gives $R_N$. If dependent sources are present, you may need a test source instead of just turning sources off."}},{"@type":"Question","name":"What is the difference between Norton and Thevenin equivalents?","acceptedAnswer":{"@type":"Answer","text":"They describe the same circuit from the same terminals, but in different forms. Norton uses a current source in parallel with a resistor, while Thevenin uses a voltage source in series with a resistor. You can convert between them using $I_N = V_{th} / R_{th}$."}},{"@type":"Question","name":"Why do dependent sources make Norton resistance harder to find?","acceptedAnswer":{"@type":"Answer","text":"Because dependent sources are controlled by circuit variables, not independent source labels, so you usually cannot just turn them off. If you do, you change the circuit behavior incorrectly. A test source method is often the safer way to find the correct terminal resistance."}}]},{"@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"name":"Electrical Circuits and Systems II","item":"https://fiveable.me/electrical-circuits-systems-ii"},{"@type":"ListItem","position":2,"name":"Key Terms","item":"https://fiveable.me/electrical-circuits-systems-ii/key-terms"},{"@type":"ListItem","position":3,"name":"Unit 7","item":"https://fiveable.me/electrical-circuits-systems-ii/unit-7"},{"@type":"ListItem","position":4,"name":"Norton Equivalent"}]}]}
```