# Theorem of Norton

The Théorème of Norton for the electrical communications establishes that any resistive circuit is equivalent to an ideal power source I , in parallel with a simple resistance R . The theorem applies to all the impedances, not only with resistances.

The statement of this theorem was published in 1926 by the engineer Edward Lawry Norton (1898-1983).

Commonly:

• the current of Norton is the current one between the terminals of the load when this one is shorted-circuit, from where Ic = I (short-circuit)
• the resistance of Norton is that measured between the terminals of the load when all the sources are made inactive while shorting-circuit the sources of tension and while disconnecting the power sources. It is noted that $R_ \ mathrm \left\{NR\right\} \ = R_ \ mathrm \left\{Th\right\} \$, with $R_ \ mathrm \left\{Th\right\} \$ the resistance of Thévenin.

## Example

• In (A): Original circuit.
• In (b): Short-circuit between the terminals has and B to find the current Norton $I_ \ mathrm \left\{NR\right\} \$

One calculation initially the total current delivered by the source of tension;
$I_ \ mathrm \left\{total\right\} = \left\{V_ \ mathrm \left\{1\right\} \ over R_ \ mathrm \left\{1\right\} + \ Bigl \left(\ dfrac \left\{R_ \ mathrm \left\{2\right\} \ cdot R_ \ mathrm \left\{3\right\}\right\} \left\{R_ \ mathrm \left\{2\right\} + R_ \ mathrm \left\{3\right\}\right\} \ Bigr\right)\right\} = 4.54 \ mathrm \left\{has\right\}$
One finds then the Current of Norton by the formula of the divider of current;
$I_ \ mathrm \left\{NR\right\} = \left\{R_ \ mathrm \left\{2\right\} \ over R_ \ mathrm \left\{2\right\} \ + R_ \ mathrm \left\{3\right\}\right\} \ cdot total I_ \ mathrm \left\{\right\} = 1.82 \ mathrm \left\{has\right\}$
• In (c): Short-circuit at the boundaries of the source of tension and open circuit between has and B to find the resistance of Norton $R_ \ mathrm \left\{NR\right\} \$

$R_ \ mathrm \left\{NR\right\} = R_ \ mathrm \left\{3\right\} + \ Bigl \left(\ dfrac \left\{R_ \ mathrm \left\{2\right\} \ cdot R_ \ mathrm \left\{1\right\}\right\} \left\{R_ \ mathrm \left\{2\right\} + R_ \ mathrm \left\{1\right\}\right\} \ Bigr\right) = 3.67 \ Omega$
• In (d): Circuit are equivalent of Norton

## External bond

• {{in}} Historique of the concept of circuit is equivalent

 Random links: Unison | Charles Ramsey | Astacidae | Cligès | Claude Ledoux | Niveau_de_vie_aux_Etats-Unis