Norton’s Theorem

Short-Circuit Current (I _N )

The short-circuit current, I _N , is the first fundamental parameter of the Norton equivalent. It is defined as the current delivered by the original circuit when its two output terminals are directly connected to each other, that is, when an ideal short circuit is made between them. Under this condition, the circuit shows its maximum current supply capability, as the external load has zero resistance. Measuring I _N captures how the circuit behaves internally when there is no external opposition to the current flow, and forms the basis of the Norton model: a current source that exactly reproduces that value.

To obtain the short-circuit current, I _N , the two terminals of the original circuit are directly connected, creating an ideal short circuit. Under this condition, the current flowing through that link is measured. That value is precisely I _N , as it represents the maximum current the circuit can deliver when the external load has zero resistance.

Equivalent Resistance Seen from the Terminals (R _N )

The equivalent resistance seen from the terminals, R _N , represents the total resistance offered by the original circuit when viewed from its two output terminals.

To obtain it, all internal sources of the circuit are “turned off”: voltage sources are replaced by short circuits and current sources by open circuits. Once this is done, the resistance between the terminals is calculated. That value is precisely R _N , and matches the equivalent resistance of Thevenin’s theorem, ensuring that both models describe the same external behavior of the circuit.

Applying the Norton Equivalent to a Load

Once I _N and R _N have been obtained, the entire network can be replaced by its Norton equivalent without the load perceiving any difference. When the load is connected to this simplified model, the current, voltage, and power it receives are exactly the same as in the original circuit, because the equivalent reproduces the current–voltage relationship the network establishes at its terminals.

The analysis becomes immediate: the current passing through the load depends only on , R _N and the resistance of the load itself, and the voltage across the load is obtained by applying the current law at the common node. This allows you to study how the system’s behavior changes when the load is modified, evaluate transferred power, or identify matching conditions without recalculating the entire internal network. Essentially, the Norton equivalent turns a complex circuit into an elementary one, keeping the response experienced by the load intact.

Relationship Between Norton and Thevenin Theorems

The Norton and Thevenin theorems describe the same electrical reality from two different but completely equivalent representations. Any linear circuit that can be expressed by a voltage source in series with a resistor (Thevenin model) can be transformed into a current source in parallel with that same resistor (Norton model), and vice versa. The conversion between them is direct: the Norton current is obtained as I _N = V _Th / R _Th and the equivalent resistance is the same in both models, R _N = R _Th . Likewise, the Thevenin equivalent is recovered from Norton’s by V _Th = I _N R _N .

This relationship ensures that both models produce exactly the same voltage, current, and power in any load connected to the terminals. The choice between one or the other depends solely on convenience in analysis. Thevenin is more natural when you are interested in studying voltages, while Norton simplifies the study of currents and current division. In any case, both theorems are two complementary ways of representing the same external behavior of a circuit.

Importance of Norton’s Theorem

Norton’s theorem is fundamental in circuit analysis because it allows a complex network to be replaced by a much simpler model without altering the response experienced by the load. This simplification is especially useful when you want to study how current is distributed at a node, how the current in the load varies when its resistance changes, or how networks behave where current division predominates. By reducing the circuit to a current source and a resistor in parallel, analysis becomes direct and transparent, avoiding repetitive calculations on the entire network.