# Norton Equivalent Circuits

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## Abstract

Connexions module: m0022 1 Norton Equivalent Circuits ∗ Don Johnson This work is produced by The Connexions Project and licensed under the Creative Commons Attribution License † Abstract Introduction of Norton equivalent circuits. As you might expect, equivalent circuits come in two forms: the voltage-source oriented Thévenin equiv- alent 1 and the current-source oriented Norton equivalent (see figure (Figure 1)). ∗ Version 2.7: Aug 10, 2004 9:36 am -0500 † http://creativecommons.org/licenses/by/1.0 1 "Finding Thévenin Equivalent Circuits" <http://cnx.org/content/m0021/latest/> http://cnx.org/content/m0022/2.7/ Connexions module: m0022 2 Figure 1: All circuits containing sources and resistors can be described by simpler equivalent circuits. Choosing the one to use depends on the application, not on what is actually inside the circuit. To derive the latter, the v-i relation for the Thévenin equivalent can be written as v = Reqi+ veq (1) or i = v Req − ieq (2) where ieq = veq Req is the Norton equivalent source. The Norton equivalent shown in the above figure (Figure 1) be easily shown to have this v-i relation. Note that both variations have the same equivalent resistance. The short-circuit current equals the negative of the Norton equivalent source. Exercise 1 (Solution on p. 4.) Find the Norton equivalent circuit for the circuit below. http://cnx.org/content/m0022/2.7/ Connexions module: m0022 3 Figure 2 Equivalent circuits can be used in two basic ways. The first is to simplify the analysis of a complicated circuit by realizing the any portion of a circuit can be described by either a Thévenin or Norton equivalent. Which one is used depends on whether what is attached to the terminals is a series configuration (making the Thévenin equivalent the best) or a parallel one (making Norton the best). Another application is modeling. When we buy a flashlight battery, either equivalent circuit can accu- rately describ

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