What is Norton's theorem?

Norton's theorem states that any linear electrical network with voltage and current sources and resistances can be represented as an equivalent current source and a parallel resistor. This theorem allows you to replace a portion of a circuit (a load) with a single current source in parallel with a resistor that provides the same current-voltage relationship as the original circuit.

The Norton equivalent circuit consists of two components:

Norton Current (In): This is the equivalent current source, denoted as In. It represents the current that would flow through a short circuit across the load terminals in the original circuit.

Norton Resistance (Rn): This is the equivalent resistance, denoted as Rn. It represents the resistance measured across the load terminals in the original circuit when all the independent sources are turned off (replaced by their internal resistances).

To find the Norton current (In) and Norton resistance (Rn), follow these steps:

Disable all independent voltage and current sources in the original circuit.

Calculate the current (In) that would flow between the load terminals if you short-circuited them together.

Calculate the resistance (Rn) measured between the load terminals when all the independent sources are turned off (replaced by their internal resistances).

Once you have determined In and Rn, you can represent the original circuit as a Norton equivalent circuit, which comprises In in parallel with Rn.

Norton's theorem is particularly useful when dealing with complex circuits, as it allows engineers to simplify and analyze parts of the circuit independently. It is also useful for finding the maximum power transfer theorem in some cases.