NORTON’S THEOREM
The theorem states the following:
Any two terminal linear bilateral dc network can be replaced by an
equivalent circuit consisting of a current source and a parallel
resistor as shown in figure.
The steps leading to the values of IN and RN are listed
Step1. Remove that portion of the network across which the Norton
equivalent circuit is found
Step2. Mark the terminals of the remaining two terminal network.
RN:
Step3. Calculate Rn by first setting all sources to zero (voltage sources
are replaced with short circuits and current sources with open
circuits) and then finding the resultant resistance between the two
marked terminals. (If internal resistance of the voltage and/or
current sources is included in the original network it must remain
when the sources are set to zero). Since RN=RTh the procedure and
value obtained using the approach described for Thevenin’s theorem
will determine the proper value for RN.
IN:
Step 4: Calculate IN by first setting all sources to their original
position and then finding the short circuit current between the
marked terminals.
Step 5. Draw the Norton equivalent circuit with the portion of the
circuit previously removed replaced between the terminals of the
equivalent circuit.
Converting between thevenin & Norton equivalent circuits
EXAMPLE 1: Find the Norton equivalent circuit for the network in
the dotted area.
SOLUTION:
Steps 1 and 2 are shown in figure:
Step 3 is shown in figure:
RN = R1 // R2 = 3Ω // 6Ω =
(3Ω)(6Ω) 18Ω
=
= 2Ω
3Ω + 6Ω
9
Step 4 is shown in the following figure clearly indicating that the
short circuit connection between terminals a and b is in parallel with
R2 and eliminates its effect. IN is therefore the same as through R1
and the full battery voltage appears across R1 since
V2 = I 2 R2 = 0(6Ω) = 0V
IN =
E 9V
=
= 3A
R1 3Ω
Step 5: See figure:
Problem: Find the Norton equivalent circuit for the network of the 9Ω
resistor
Solution : steps 1 & 2:
Step 3:
R N = R1 + R2 = 5Ω + 4Ω = 9Ω
Step 4:
The Norton current is the same as the current through the 4W resistor.
Applying the current divider rule:
IN =
R1 I
(5Ω)(10 A)
=
= 5.556 A
R1 + R2
5Ω + 4Ω
Step 5:
Substituting the Norton equivalent circuit for the network external to the
resistor RL