--- title: "Norton Resistance | Electrical Circuits II" description: "Norton resistance is the equivalent resistance seen looking into a circuit with independent sources turned off, used to simplify AC analysis in Circuits II." canonical: "https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-resistance" type: "key-term" subject: "Electrical Circuits and Systems II" unit: "Unit 1" --- # Norton Resistance | Electrical Circuits II ## Definition Norton resistance is the equivalent resistance seen looking back into a circuit after independent sources are turned off. In Electrical Circuits and Systems II, it is used to simplify AC and linear circuit analysis. ## What It Is Norton resistance is the resistance you see when you look into a linear circuit from the load terminals after removing the load and turning off all independent sources. In Electrical Circuits and Systems II, that means you replace independent voltage sources with shorts and independent current sources with opens, then find the equivalent resistance seen from those terminals. The idea is not to measure every resistor one by one. You are collapsing the rest of the network into one value that describes how hard it is for current to flow from the point where the load connects. If the circuit is purely resistive, that value is just an ordinary resistance. If the circuit is in steady-state AC, the same idea extends to impedance, so the equivalent seen by the load can be complex. This term shows up when you are building a Norton equivalent. The Norton model uses a current source in parallel with Norton resistance, which lets you replace a messy circuit with a simpler two-part model. Once you have that equivalent, finding load current or load voltage becomes much easier, especially if the original circuit has several branches. A common move is to remove the load, deactivate the independent sources, and then simplify the remaining network with series-parallel reduction, nodal analysis, mesh analysis, or test-source methods if the circuit is not reducible by inspection. In AC work, you do the same thing with impedances, not just plain resistors, so capacitors and inductors affect the result through their reactances. One thing that trips people up is mixing up source deactivation with source removal. You do not delete the source from the schematic entirely, you replace it with its internal zero value for the purpose of finding the equivalent. Dependent sources are different, since they stay active and often require a test source to compute the resistance correctly. ## Why It Matters Norton resistance gives you a fast way to simplify a circuit before you calculate what the load receives. In Electrical Circuits and Systems II, that matters because many problems are not about the whole network, they are about one output branch, one sensor, or one load resistor connected to a larger system. It also connects directly to steady-state AC analysis. Once resistors are replaced by impedances, a load may be connected to a source network that includes inductive reactance and capacitive reactance, and Norton resistance becomes the equivalent impedance seen at the terminals. That lets you predict current sharing and voltage drop without re-solving the full circuit every time the load changes. You will also see it in conversion between Norton and Thevenin forms. If you know the Norton current and Norton resistance, you can convert to a Thevenin source and use whichever model makes the algebra easier. That flexibility is useful in homework, lab writeups, and any problem where the instructor wants the load behavior rather than the internal details of the source network. The bigger skill here is terminal thinking. Instead of staring at the whole schematic, you ask, "What does the load see from these two nodes?" That perspective shows up again in two-port networks, maximum power transfer, and frequency-response work later in the course. ## Connections ### Thevenin Resistance Thevenin resistance and Norton resistance describe the same terminal behavior for a linear circuit. You find one from the other through source conversion, so if a problem is easier in Thevenin form, you can still get the Norton form without starting over. Students often use whichever equivalent makes the load calculation cleaner. ### Norton’s Theorem Norton’s Theorem is the full equivalent-circuit method that pairs a current source with Norton resistance. Norton resistance is only one part of the model, but it is the piece that sets the parallel branch behavior. If you can find this resistance correctly, the rest of the theorem becomes straightforward. ### AC Circuit Analysis In steady-state AC circuit analysis, resistance becomes impedance when inductors and capacitors are present. Norton resistance in this setting is really the equivalent impedance seen at the terminals after source deactivation. That is why phasors and complex numbers matter, not just plain resistor sums. ### [Maximum Power Transfer Theorem](/electrical-circuits-systems-ii/key-terms/maximum-power-transfer-theorem) Maximum power transfer problems often use Norton or Thevenin equivalents because the load condition is easier to express at the terminals. Norton resistance tells you the source-side equivalent the load is matched against. Once you know it, you can compare the load value to the source equivalent and check whether the match condition is satisfied. ## On the AP Exam A problem set question may give you a circuit and ask for the Norton equivalent seen by a load. Your job is to remove the load, turn off independent sources, and compute the resistance or impedance looking into the open terminals. If the circuit has dependent sources, you usually keep them active and use a test source instead of trying to turn everything off. You may also be asked to use Norton resistance to find load current after the circuit is simplified. In AC problems, expect complex impedances, so you need to keep track of magnitude and phase, not just the numeric value of resistance. The common mistake is forgetting to deactivate only independent sources, or forgetting that inductors and capacitors contribute frequency-dependent reactance in steady-state AC. ## Norton Resistance vs Thevenin Resistance These two are the most common comparison because they describe the same terminal resistance from two equivalent circuit forms. Thevenin resistance is used with a voltage source in series, while Norton resistance is used with a current source in parallel. For a linear circuit, they convert directly into each other. ## Key Takeaways - Norton resistance is the equivalent resistance or impedance seen looking into a circuit after the load is removed and independent sources are turned off. - In steady-state AC analysis, you find the same terminal value using complex impedances, not just simple resistor arithmetic. - The value becomes the parallel resistance in the Norton equivalent model, so it controls how the source network interacts with the load. - Dependent sources are not turned off, which means some circuits require a test source to get the correct Norton resistance. - If you know Norton resistance, you are one step away from a full Norton or Thevenin equivalent and a much simpler load calculation. ## FAQs ### What is Norton resistance in Electrical Circuits and Systems II? It is the equivalent resistance or impedance seen at the output terminals of a circuit after you remove the load and deactivate all independent sources. In this course, it is used to build a Norton equivalent for easier AC or DC analysis. The idea is to replace a complicated network with one value that describes how the network behaves from the load’s point of view. ### How do you find Norton resistance? First remove the load from the circuit. Then turn off independent voltage sources by replacing them with shorts and independent current sources by replacing them with opens, and simplify the network seen from the terminals. If dependent sources are present, you usually need a test source method instead of only series-parallel reduction. ### Is Norton resistance the same as Thevenin resistance? Yes, for any linear circuit they are the same terminal resistance seen from the load. The difference is the equivalent model you pair it with, current source for Norton and voltage source for Thevenin. That is why you can convert between the two forms once you know the resistance. ### Do capacitors and inductors change Norton resistance? In steady-state AC, yes, because you work with impedance instead of plain resistance. Capacitive reactance and inductive reactance affect the equivalent seen at the terminals, and the result can have both magnitude and phase. That is why Norton resistance in AC problems is often a complex impedance. ## 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) ## 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-resistance#resource","name":"Norton Resistance | Electrical Circuits II","url":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-resistance","learningResourceType":"Concept explainer","educationalLevel":"AP® / High School","about":{"@id":"https://fiveable.me/electrical-circuits-systems-ii/key-terms/norton-resistance#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-resistance#term","name":"Norton Resistance","description":"Norton resistance is the equivalent resistance seen looking back into a circuit after independent sources are turned off. 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