Module 1: DC Circuits
Basic Electrical Engineering
Jayanta Bhusan Basu
Norton’s Theorem
Like Thevenin's Theorem, in Norton's Theorem any complex linear circuit can be represented by an equivalent circuit
with just a single current source and parallel resistance connected to a load. As it has been observed earlier that any
voltage source in series with a resistance can be converted to a current source having an equal resistance in parallel
with the source, Norton's theorem is basically an application of that. If we convert the Thevenin's equivalent circuit
which actually is having a voltage source (Thevenin Voltage) in series with a resistance (Thevenin Resistance) to an
equivalent current source, we will get the Norton's equivalent circuit.
Norton's theorem states that
The current through a load resistance'
L
R
' across any two load terminals of a linear active bilateral network is
given by N N
N L
I R
R R
, Where IN is the Short circuit Current Through the load terminals termed as Norton Current
& RN is the equivalent open circuited resistance(termed as Norton resistance ) of the network when viewed
from the load terminals, While measuring RN all the sources of the network is to be replaced by their internal
resistances. The value of RN is equal to that of RTH.
The Norton's equivalent circuit is shown in figure
Circuit explaining Norton’s theorem
The steps for finding Norton's equivalent circuit across any two load terminals are:
Step-1: Disconnect the load resistor from the original network.
Step-2: Find the Norton source current by measuring the short circuit current through a short placed across
the load terminals after removing the load resistor.
Step-3: Find the Norton resistance similarly to that of Thevenin Resistance.
Step-4: Draw the Norton equivalent circuit, with the Norton Current source in parallel with the Norton
resistance.
Step 5: Reconnect the load resistor between the two open load terminals of the equivalent circuit.
Step 6: Find the current for the load resistor following the rules for parallel circuits given by
N
L N
N L
R
I I
R R
Some equivalencies of Thevenin's & Norton's Theorem
Thevenin Resistance ' ' Norton Resistance
' '
TH N
R R
Thevenin Voltage 'V '
TH N N
I R
Norton Current 'I '
TH
N
TH
V
R
