Norton Current from the Thevenin Equivalent

Edward Norton at Bell Labs described the dual of Thévenin's result in 1926: the same two terminals can equally be modelled as a current source with a resistor in parallel. The two models are interchangeable, and the bridge between them is Ohm's law — a 12 V source behind 4 Ω is a 3 A source across 4 Ω, and no measurement made at the terminals can tell them apart.

Which one you pick is pure convenience. Norton form makes parallel branches trivial, because current sources in parallel simply add, so it is the natural language of nodal analysis and of transistor models. Thevenin form makes series chains trivial. Experienced analysts flip back and forth mid-problem — that flip is called a source transformation, and it is often the single step that turns an ugly network into an obvious one.

The number I_N is the current the source would deliver into a dead short, which is worth respecting. A 12 V car battery with 5 mΩ internal resistance has a Norton current of 2400 A, and that is why a dropped spanner across the terminals vaporises. Note also that both models are fictions from the terminals only: a Norton equivalent burns power in its resistor even at no load, so it tells you nothing true about what the real box is dissipating inside.