Norton's Theorem

Thevenin's equivalent circuit is a practical voltage source. In contrast, Norton's equivalent circuit is a practical current source. This can be formally stated as

"Any 2-terminal, linear circuit, of resistors and sources, is replaced by a single current source in parallel with a resistor."

To determine Norton's equivalent circuit, Norton current, IN, and Norton resistance, RN, are required. The following steps depicts the process required.

1. Remove load resistance, RL.

2. I_N is SC current through the load terminals and

3. R_N is the resistance across the load terminals with all sources replaced by their internal resistances. Clearly R_N =R_TH.

Example

For = circuit diagram shown in Figure, use Norton's theorem to determine current through the 5Ωresistance. As mentioned above, The Norton's resistance is same as Thevenin's resistance, that is
 

To find out Norton's current, terminals A and B in Figure (b) are short circuited. Then the current through the short circuited terminals is Norton current, I_N or I_sc.
 
There are a number of ways to solve above circuit like KVL, KCL, but, circuit reduction techniques have been chosen here. Firstly, total current supplied by voltage source can be found by adding resistances using Series or parallel combination.

 
Since Is I₁0Ω,I_sc can be found by employing CDR between 15Ω and 20Ω resistances that is
 
The Norton's equivalent circuit is drawn as shown in Figure given below
 

Norton's equivalent circuit for the Figure given above across the 5Ω load. The current through the resistance is determined by the application of CDR between R_L and R_N, thus

 
which tallies with result when Thevenin's theorem was employed.

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