4. NORTON THEOREM NUMERICALS | PROBLEM 3 | BASIC ELECTRONICS | SECRETS OF PHYSICS | RABIA BABER

Описание: NORTON THEOREM
Norton’s theorem is a useful method in circuit analysis that helps you simplify a complicated electrical network into a very simple equivalent form. It says that any linear, two-terminal circuit (containing sources and resistors, or in AC, impedances) can be replaced by an equivalent circuit made of one current source in parallel with one resistance. This replacement is done only with respect to two chosen terminals, usually the terminals where the load is connected. After replacement, the load will receive the same current and voltage as it would in the original circuit.
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The Norton equivalent has two main terms:

Norton current: This is the current source value in the equivalent circuit. It is found by shorting the two terminals (connecting them with a wire) and calculating the current that flows through that short. That short-circuit current becomes the Norton current.
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Norton resistance: This is the resistance connected in parallel with the current source. To find it, you turn off all independent sources in the circuit and then calculate the resistance seen from the two terminals. Turning off sources means: replace an independent voltage source with a short connection, and replace an independent current source with an open connection. Then you find the equivalent resistance looking into the network from the terminals; that is the Norton resistance.
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A very important rule is about dependent sources (controlled sources). Dependent sources should not be turned off, because their values depend on circuit variables. If dependent sources exist, Norton resistance is often found by applying a test source at the terminals and observing the response to determine the resistance seen.
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Norton’s theorem is closely related to Thevenin’s theorem. Thevenin gives an equivalent of a voltage source in series with a resistance, while Norton gives a current source in parallel with a resistance. Both equivalents represent the same original circuit behavior at the terminals, and the resistance value is the same in both methods. You can also convert between Norton and Thevenin forms when needed.
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Norton’s theorem is especially helpful when you want to find load current easily, or when the circuit naturally has many parallel branches. Once the Norton equivalent is found, changes in load resistance become easier to study without solving the full circuit again. This saves time and reduces mistakes.
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In short, Norton’s theorem is a powerful shortcut that converts a complex linear network into a simple parallel current-source model, making circuit calculations faster and clearer.
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