What is Norton's theorem?

The theorem that a circuit of sources and linear elements, seen from a pair of terminals, can be replaced by a single current source Isc in parallel with a single impedance Zth. Isc is the current with the terminals shorted, and Zth is the same as in the Thevenin equivalent. It converts to and from the Thevenin equivalent through Vth = Zth × Isc, and is convenient for loads connected in parallel and for circuits with current sources.

Japanese name: ノートンの定理

Norton's theorem appears in 3 practice questions across 3 topics, including Circuit and electromagnetism basics, Circuit Analysis: AC, Linear Circuits and Transients, Analog and electronic circuits.

Field: Circuit Analysis: AC, Linear Circuits and Transients

Try it: questions about Norton's theorem

Which Norton equivalent (current source and resistor) is equivalent to a voltage source with an EMF of 12 V and an internal resistance of 4 Ω?

AA 3 A current source with 4 Ω in parallel
BA 3 A current source with 4 Ω in series
CA 48 A current source with 4 Ω in parallel

Show answer and explanation

Answer: A. A 3 A current source with 4 Ω in parallel

The Norton current source equals the current that flows when the terminals are shorted: 12 V/4 Ω = 3 A. The resistor is the same 4 Ω as the Thevenin resistance and goes in parallel with the current source. As a check, with the terminals open all 3 A flows through the 4 Ω, giving 3 A × 4 Ω = 12 V—the open-circuit voltage of the original source. Converting between voltage and current sources is a common way to simplify circuits.

Norton's theorem in the explanations

As a Norton equivalent, it is a current source equal to the current with the terminals shorted, E/R1 + J = 5 A, in parallel with 4 Ω.
In the circuit in the figure, E = 12 V, R1 = 4 Ω and J = 2 …
Replacing it with a current source and parallel resistor is Norton's theorem.
Which correctly states Thevenin's theorem?

Questions that mention Norton's theorem (3)

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