Norton's theorem
A theorem which states that any electric circuit between two terminals containing only resistors, voltage sources, and current sources can be equivalently replaced with a single current source and resistor in parallel.
Norton's theorem: swap any circuit for one current source
Norton's theorem lets you replace a complex network of resistors, voltage sources, and current sources with a single equivalent circuit: a current source IN in parallel with a resistance RN. The two terminals where you connect a load see identical voltage and current behavior before and after the swap. This is the dual of Thévenin's theorem, which uses a voltage source and series resistance instead.
To find the Norton equivalent, calculate two values. First, the Norton current is the short-circuit current that flows between the terminals when they are connected together with a wire. Second, the Norton resistance is the resistance seen looking back into the network from those terminals with all independent sources killed (voltage sources become short circuits; current sources become open circuits). Some circuits also contain dependent sources, which must be retained during this calculation, making the algebra more complex.
When to use Norton's theorem
Norton conversion shines when you need to analyze how a load resistor behaves as it varies. Rather than recalculating the entire network for each load value, you calculate the Norton equivalent once, then model the load against this simple two-component circuit. This saves time in hand calculation and is especially useful for maximum power transfer problems, where the load must equal the source resistance to extract maximum watts.
The theorem applies strictly to linear circuits. If the network contains diodes, transistors, or other nonlinear components, Norton's theorem does not hold. It also assumes that the two terminals are not inside a loop where energy is being transferred magnetically to another part of the circuit; mutual inductance breaks the method.
Named after Edward Lowry Norton, who published the concept in 1926, the theorem is mathematically equivalent to Thévenin's theorem published by Léon Charles Thévenin in 1883. Engineers choose between them based on whether a current or voltage source fits the problem more naturally. Software for circuit simulation computes Norton equivalents automatically, but understanding the concept remains essential for debugging and for hand analysis of filter networks, impedance matching, and amplifier loading effects.