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 I_c = 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 {NR} \ = R_ \ mathrm {Th} \$ , with $R_ \ mathrm {Th} \$ 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 {NR} \$

One calculation initially the total current delivered by the source of tension;

I_ \ mathrm {total} = {V_ \ mathrm {1} \ over R_ \ mathrm {1} + \ Bigl (\ dfrac {R_ \ mathrm {2} \ cdot R_ \ mathrm {3}} {R_ \ mathrm {2} + R_ \ mathrm {3}} \ Bigr)} = 4.54 \ mathrm {has}

One finds then the Current of Norton by the formula of the divider of current;

I_ \ mathrm {NR} = {R_ \ mathrm {2} \ over R_ \ mathrm {2} \ + R_ \ mathrm {3}} \ cdot total I_ \ mathrm {} = 1.82 \ mathrm {has}

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 {NR} \$

R_ \ mathrm {NR} = R_ \ mathrm {3} + \ Bigl (\ dfrac {R_ \ mathrm {2} \ cdot R_ \ mathrm {1}} {R_ \ mathrm {2} + R_ \ mathrm {1}} \ Bigr) = 3.67 \ Omega

In (d): Circuit are equivalent of Norton

See too

Electricity
Theorem of Thévenin
Law of Ohm
Laws of Kirchhoff (law of the meshs and law of the nodes)
Principle of superposition
Theorem of Millman
Theorem of reciprocity

External bond

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

Random links: