Formula & Calculator
Norton's Theorem Equivalent Current
Any linear two-terminal network can be replaced by an equivalent current source in parallel with a resistance.
Interpretation
Norton's theorem: any linear two‑terminal circuit can be replaced by a current source (I_N) in parallel with a resistance (R_N).
I_N is the short‑circuit current measured at the output terminals.
Example: If you short the output terminals and measure 2A, then I_N = 2A.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| I_N | Norton equivalent current | A |
| I_SC | Short-circuit current | A |
What it means
Norton’s theorem states that any linear two‑terminal circuit can be replaced by an equivalent current source (I_N) in parallel with a resistance (R_N). The Norton current I_N is the short‑circuit current that would flow between the two terminals when they are shorted. The Norton resistance R_N is the equivalent resistance seen looking back into the terminals with all independent sources deactivated (voltage sources shorted, current sources opened). This theorem is the dual of Thévenin’s theorem and is especially useful for parallel‑connected loads. It simplifies the analysis of circuits where the load is variable, as the equivalent circuit remains fixed. Norton’s theorem is used in power systems for fault analysis, in amplifier design for output impedance calculations, and in sensor interfacing. The relationship between Norton and Thévenin equivalents is V_TH = I_N * R_N and R_TH = R_N. Example: If the short‑circuit current measured at the terminals is 2A, then I_N = 2A. The Norton equivalent is a 2A current source in parallel with R_N.
Worked example
Norton's Theorem – Practical Example
Real‑World| Parameter | Value |
|---|---|
| Short‑circuit current (ISC) | 2 A |
| Formula | IN = ISC |
Common mistakes
- Norton current I_N: The short‑circuit current at the terminals – not the open‑circuit voltage.
- Resistance R_N: The equivalent resistance seen from the terminals with all independent sources turned off (voltage sources shorted, current sources open).
- Dependent sources: Keep them active when computing R_N – use a test source method.
- Polarity: The current source direction is defined by the short‑circuit current direction.
- Source transformation: Norton and Thevenin equivalents are interchangeable via V_TH = I_N·R_N.
Applications
Norton's theorem states that any linear two‑terminal circuit can be replaced by a current source (I_N) in parallel with a resistance (R_N). I_N is the short‑circuit current, and R_N is the equivalent resistance seen from the terminals. This theorem simplifies circuit analysis, especially when dealing with variable loads. Engineers use it to simplify power source models, to analyse parallel circuits, and to design maximum power transfer. By converting a network to its Norton equivalent, they can quickly determine load current and voltage. Norton's theorem is complementary to Thévenin's theorem and is widely used in circuit simulation and teaching. Understanding Norton's theorem is essential for efficient circuit analysis and design.
- Simplification of complex networks for analysis
- Source modelling for current sources and sensors
- Maximum power transfer and load matching
- Circuit simulation and symbolic analysis
- Educational foundation of network theorems
Frequently Asked Questions
Norton's theorem states that any linear two-terminal network can be replaced by a current source I_N in parallel with a resistance R_N. The Norton current I_N is the short-circuit current at the terminals.
Short-circuit the output terminals and calculate the current flowing through the short circuit. That current is I_N.
Deactivate all independent sources (voltage sources become short circuits, current sources become open circuits) and calculate the equivalent resistance seen from the output terminals.
Thevenin voltage V_TH = I_N × R_N, and R_TH = R_N. They are duals and can be converted.
No, it is only valid for linear circuits. Non-linear elements must be linearized around an operating point.
Simplifying complex circuits for analysis, especially in power systems and amplifier design.
Dependent sources remain active when calculating R_N, but they must be handled with care; the resistance is found by applying a test voltage/current.
Maximum power is delivered to a load when R_L = R_N (same as Thevenin).
Norton uses a current source in parallel with resistance; Thevenin uses a voltage source in series with resistance.
Common errors include: 1) incorrectly calculating the short-circuit current, 2) deactivating sources incorrectly, 3) confusing with Thevenin, 4) applying to non-linear circuits, and 5) using the wrong equivalent circuit topology.