---
title: "Norton's Theorem | Principles of Physics II"
description: "Norton's Theorem replaces a linear circuit with a current source in parallel with a resistor, making circuit and load calculations easier in Physics II."
canonical: "https://fiveable.me/principles-physics-ii/key-terms/nortons-theorem"
type: "key-term"
subject: "Principles of Physics II"
unit: "Unit 4"
---

# Norton's Theorem | Principles of Physics II

## Definition

Norton's Theorem says any linear circuit can be replaced by an equivalent current source in parallel with a resistor. In Principles of Physics II, you use it to simplify circuit analysis and find the current through a load.

## What It Is

Norton's Theorem is a circuit simplification method in Principles of Physics II. It lets you replace a complicated linear network with one equivalent current source in parallel with one equivalent resistor.

The idea is not that the original circuit disappears, but that its effect on the two terminals you care about can be matched by a much simpler model. If the original network and the Norton equivalent give the same terminal current and voltage for any load, then they behave the same from the outside.

To build the Norton equivalent, you first find the short-circuit current across the terminals. That current becomes the Norton current, often written as I_N. Then you find the equivalent resistance, R_N, seen looking back into the circuit after turning off independent sources. Voltage sources become shorts, and current sources become opens. The resistor you get is placed in parallel with the current source.

This theorem works for both DC and AC circuits, as long as the network is linear. In AC problems, the resistance may become an impedance, so the same method applies with complex circuit elements. That is why Norton analysis shows up in more advanced circuit problems, not just simple resistor networks.

A good way to picture it is as a device that answers one question: what current can this network deliver to a load at its terminals? Once you have I_N and R_N, you can attach a load resistor and use current division or Ohm’s law to find the load current much faster than solving the whole original circuit again.

## Why It Matters

Norton's Theorem matters because circuit problems in Physics II often focus on what happens at two terminals, not on every internal branch at once. If you can replace a messy network with a current source and one resistor, the rest of the problem becomes a one-step calculation instead of a multi-equation setup.

This is especially useful for load analysis. If a resistor, sensor, or other component is attached to the output terminals, you can quickly predict how much current it draws and how the terminal voltage changes when the load changes. That makes Norton form a practical tool for comparing circuits with different loads.

It also deepens your understanding of equivalence. Norton and Thevenin forms are two different views of the same linear circuit, so you start seeing that circuit analysis is often about finding the right representation, not just grinding through algebra. In later electromagnetism or electronics-style problems, that habit saves time and reduces mistakes.

The theorem also connects directly back to Ohm's law, since the equivalent resistor still sets the relationship between voltage and current at the terminals. In other words, Norton does not replace Ohm’s law, it gives you a cleaner circuit to use it on.

## Connections

### [Thevenin's Theorem](/principles-physics-ii/key-terms/thevenins-theorem)

Thevenin's Theorem is the closest companion to Norton form. Instead of a current source in parallel with a resistor, Thevenin uses a voltage source in series with a resistor. They describe the same linear circuit at the same terminals, so you can convert between them depending on which form makes the load calculation easier.

### Equivalent Circuit

A Norton equivalent is a type of equivalent circuit, meaning it preserves the terminal behavior of the original network without preserving every internal detail. In Physics II, equivalent circuits show up when you care about what a component sees from the outside, especially when a load is attached.

### Superposition Theorem

Superposition is often one route to finding the Norton current in a circuit with multiple sources. You can analyze the effect of each independent source one at a time, then combine the results to get the total short-circuit current. That makes Norton analysis easier in source-rich networks.

## On the AP Exam

A quiz or problem-set question usually asks you to find the Norton equivalent across two terminals, then use it to determine the current through a load resistor. The move is: isolate the terminals, compute the short-circuit current for I_N, turn off independent sources to get R_N, then rebuild the simplified circuit and apply current division or Ohm's law.

You may also be asked to compare Norton and Thevenin forms or convert one into the other. If the problem includes a graph or circuit diagram, be ready to identify the terminals correctly, since the equivalent depends on which two points you are looking into. A common mistake is to find the resistance of the whole circuit instead of the resistance seen from the terminals after sources are deactivated.

## Norton's Theorem vs Thevenin's Theorem

Norton and Thevenin are often confused because they describe the same linear circuit in two different forms. Norton uses a current source in parallel with a resistor, while Thevenin uses a voltage source in series with a resistor. If you know one equivalent, you can convert to the other using the source resistance relationship.

## Key Takeaways

- Norton's Theorem turns a linear circuit into a current source in parallel with a resistor.
- The Norton current is the short-circuit current between the two output terminals.
- The Norton resistance is the resistance seen from those terminals after independent sources are turned off.
- This theorem is especially useful when you want the current through a load attached to the circuit.
- Norton and Thevenin describe the same circuit, just in different equivalent forms.

## FAQs

### What is Norton's Theorem in Principles of Physics II?

It is a method for replacing a linear circuit with an equivalent current source in parallel with a single resistor. In Physics II, that makes it much easier to find terminal current and load current without solving the full circuit every time.

### How do you find the Norton current?

You short the output terminals and calculate the current that flows through that short. That short-circuit current is the Norton current, I_N. It tells you how much current the original network can supply at the terminals.

### How do you find the Norton resistance?

Turn off all independent sources, then look into the circuit from the terminals and calculate the equivalent resistance. Voltage sources are replaced by shorts and current sources by opens. The resistance you see is R_N.

### Is Norton's Theorem the same as Thevenin's Theorem?

They are equivalent descriptions of the same linear circuit, but the forms look different. Norton uses current source plus parallel resistor, while Thevenin uses voltage source plus series resistor. You can convert between them when one form is easier for the problem.

## Related Study Guides

- [4.5 Ohm's law](/principles-physics-ii/unit-4/ohms-law/study-guide/gvnaGOeNhwbg0ZXQ)

## About This Document

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