--- title: "Norton's Theorem | Electrical Circuits II" description: "Norton's Theorem replaces a linear network with a current source in parallel with a resistor, making Electrical Circuits and Systems II circuit analysis faster." canonical: "https://fiveable.me/electrical-circuits-systems-ii/key-terms/nortons-theorem" type: "key-term" subject: "Electrical Circuits and Systems II" unit: "Unit 1" --- # Norton's Theorem | Electrical Circuits II ## Definition Norton's Theorem says any linear two-terminal circuit can be replaced by an equivalent current source in parallel with a resistor. In Electrical Circuits and Systems II, you use it to simplify AC or DC network analysis at a pair of terminals. ## What It Is Norton's Theorem is a circuit simplification method that turns a complicated linear network into a much simpler equivalent: one current source in parallel with one resistor. The “network” can include resistors, independent sources, and in AC steady-state, impedances written in phasor form. What matters is that the circuit is linear, so its terminal behavior can be preserved by an equivalent source-resistor pair. In Electrical Circuits and Systems II, you usually apply Norton’s form when you care about what happens at two terminals, like the terminals feeding a load. Instead of solving the full circuit every time the load changes, you replace everything seen from those terminals with its Norton equivalent. Then the load current and load voltage come from a much smaller circuit. The Norton current, usually written as I_N, is the short-circuit current between the two terminals. That means you temporarily connect the output terminals with a wire and calculate the current through that short. The Norton resistance, R_N, is the resistance seen looking back into the circuit after you turn off all independent sources, voltage sources become shorts and current sources become opens. In AC problems, that resistance step becomes an impedance calculation, so the equivalent may be complex. A common shortcut is that Norton and Thevenin forms are two versions of the same equivalent. Once you find one, you can convert using V_Th = I_N R_N and I_N = V_Th / R_N. So if a problem is easier with one form, you are not locked into it. A compact example makes the idea clearer. Suppose a network seen at two terminals has a short-circuit current of 3 A and a Norton resistance of 6 ohms. Its Norton equivalent is a 3 A source in parallel with 6 ohms. If you attach a 6 ohm load, the load sits in parallel with the source resistor, and current division gives the load current without re-solving the original network. The biggest trap is forgetting that the theorem only works for linear circuits. If the circuit has nonlinear elements, like a diode operating outside a linear model, the simple Norton replacement no longer holds exactly. Another common mistake is using the wrong terminals, because the equivalent is defined from the point of view of the load connection you choose. ## Why It Matters Norton’s Theorem gives you a repeatable way to shrink a messy circuit into something you can analyze fast. That matters most when the question is not “What does the whole network do?” but “What current or voltage appears at these terminals when I connect a load?” In Electrical Circuits and Systems II, you see this again and again in AC steady-state problems, where the circuit elements are impedances and the algebra gets heavier. A Norton equivalent lets you separate the source network from the load. That makes it easier to compare loads, find maximum power conditions, or check how a change in one component affects terminal behavior. The theorem also connects directly to the way you think about real circuits. Many practical devices are modeled as a source with an internal resistance or impedance, and Norton form matches current-driven behavior especially well. If you are working with current output stages, sensor models, or parallel-connected loads, the Norton picture often feels more natural than a voltage-source view. It also reinforces a big idea from this course: different circuit representations can describe the same terminal behavior. That idea shows up later in equivalent circuits, two-port thinking, and frequency-domain analysis. If you can move comfortably between the original network, Norton form, and Thevenin form, you can pick the setup that makes the math cleanest instead of forcing one method every time. ## Connections ### [Thevenin's Theorem](/electrical-circuits-systems-ii/key-terms/thevenins-theorem) Thevenin’s Theorem is the voltage-source version of the same idea. It replaces a linear network with a voltage source in series with a resistance or impedance, while Norton uses a current source in parallel with a resistance or impedance. If one form is easier to compute, you can convert to the other using simple source-resistance relationships. ### Equivalent Circuit Norton’s Theorem is one specific kind of equivalent circuit. The whole point is to preserve the terminal behavior of the original network while simplifying the internal details. In problem solving, this lets you keep the load the same and swap out only the complicated source network behind the terminals. ### [Norton Resistance](/electrical-circuits-systems-ii/key-terms/norton-resistance) Norton resistance is the single resistor or impedance that sits in parallel with the Norton current source. You find it by turning off independent sources and looking into the terminals, or by using I_N and V_Th if you already know one equivalent form. Students often confuse this with the load resistance, but they are not the same thing. ### [Norton Current](/electrical-circuits-systems-ii/key-terms/norton-current) Norton current is the short-circuit current at the output terminals. It is the source value in the Norton equivalent and gives you the current that the network would deliver if the terminals were directly shorted. In many problems, finding this current is the first step before building the full equivalent. ## On the AP Exam A quiz or problem-set question will usually give you a circuit and ask for the Norton equivalent seen at two terminals. Your job is to find the short-circuit current, determine the equivalent resistance or impedance with independent sources turned off, and redraw the circuit as a current source in parallel with that resistance. After that, you may be asked for load current, load voltage, or power, so you use current division or Ohm’s law on the simplified circuit. In AC steady-state problems, the same process happens with phasors and impedances instead of plain resistors. The tricky part is keeping track of source suppression correctly and using the right terminal pair. If you can identify where the load connects, Norton’s Theorem turns a long circuit-analysis question into a short calculation chain. ## Norton's Theorem vs Thevenin's Theorem These two are the most common pair students mix up because they describe the same linear network from different angles. Norton uses a current source in parallel with a resistor, while Thevenin uses a voltage source in series with a resistor. If a problem gives you short-circuit current, Norton usually feels natural; if it gives you open-circuit voltage, Thevenin often feels faster. ## Key Takeaways - Norton’s Theorem replaces a linear two-terminal network with a current source in parallel with a resistor or impedance. - The Norton current is the short-circuit current at the terminals, and the Norton resistance is found by looking into the circuit with independent sources turned off. - In AC steady-state analysis, the same idea works with phasors and impedances, not just plain resistors. - Norton and Thevenin are equivalent descriptions of the same terminal behavior, so you can convert between them when it makes the math easier. - The theorem only works for linear circuits, so nonlinear devices do not fit the simple Norton model exactly. ## FAQs ### What is Norton's Theorem in Electrical Circuits and Systems II? It is a method for replacing any linear two-terminal circuit with a current source in parallel with a resistor or impedance. You use the equivalent to analyze the load at those terminals without solving the full network again. It works in both DC and AC steady-state circuits. ### How do you find the Norton equivalent? First find the short-circuit current between the terminals, which gives you I_N. Then turn off all independent sources and find the resistance or impedance seen looking into the terminals to get R_N. Put those two parts together as a current source in parallel with the resistance. ### What is the difference between Norton and Thevenin? They describe the same circuit behavior 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. The choice usually depends on which quantity is easier to calculate first. ### When do you use Norton's Theorem on homework problems? Use it when a problem asks for the current, voltage, or power at a load connected to a complicated linear circuit. It is especially useful when the load changes and you want to avoid redoing the whole analysis. In AC problems, it also keeps the algebra cleaner by working directly with impedances. ## Related Study Guides - [1.4 Steady-state AC circuit analysis techniques](/electrical-circuits-systems-ii/unit-1/steady-state-ac-circuit-analysis-techniques/study-guide/7WINs6MIimU9qgF4) - [9.1 Operational amplifier fundamentals](/electrical-circuits-systems-ii/unit-9/operational-amplifier-fundamentals/study-guide/BFHOQXvNvSU5QiNs) ## 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/nortons-theorem#resource","name":"Norton's Theorem | Electrical Circuits II","url":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/nortons-theorem","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/nortons-theorem#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/nortons-theorem#term","name":"Norton's Theorem","description":"Norton's Theorem says any linear two-terminal circuit can be replaced by an equivalent current source in parallel with a resistor. 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