Norton's Theorem:
Statement:
Nortons theorem states that “a linear two terminal circuit can be replaced by an equivalent current source IN in parallel with a resistance RN where RN is the equivalent resistance at the terminals and IN is the short circuit current through the terminals where all the independent sources are not effected by the terminals”.
Properties of Norton's Theorem:
In order to find the current through the load resistance IL as shown in the circuit diagram above, the load resistance has to be short-circuited as shown in the diagram below
And the short-circuit current Isc is given by the equation shown below
Now the short circuit is removed, and the independent source is deactivated as shown in the circuit diagram below and the value of the internal resistance is calculated by
As per the Norton’s Theorem, the equivalent source circuit would contain a current source in parallel to the internal resistance, the current source being the short-circuited current across the shorted terminals of the load resistor. The Norton’s Equivalent circuit is represented as
Statement:
Nortons theorem states that “a linear two terminal circuit can be replaced by an equivalent current source IN in parallel with a resistance RN where RN is the equivalent resistance at the terminals and IN is the short circuit current through the terminals where all the independent sources are not effected by the terminals”.
Properties of Norton's Theorem:
- These Theorems are applicable only for linear R, L, C, Transformer and linear controlled sources as elements.
- Presents of dependent sources makes the network active and hence these theorems are used for both active as well as passive networks.
Explanation of Norton’s Theorem:
To understand the Norton’s Theorem in detail, let us consider a circuit diagram given below
In order to find the current through the load resistance IL as shown in the circuit diagram above, the load resistance has to be short-circuited as shown in the diagram below
Now, the value of current I flowing in the circuit is found out by the equation
And the short-circuit current Isc is given by the equation shown below
Now the short circuit is removed, and the independent source is deactivated as shown in the circuit diagram below and the value of the internal resistance is calculated by
As per the Norton’s Theorem, the equivalent source circuit would contain a current source in parallel to the internal resistance, the current source being the short-circuited current across the shorted terminals of the load resistor. The Norton’s Equivalent circuit is represented as
Finally the load current IL calculated by the equation shown below
Where,
- IL is the load current
- Isc is the short circuit current
- Rint is the internal resistance of the circuit
- RL is the load resistance of the circuit
Steps for Solving a Network Utilizing Norton’s Theorem
Step 1: Remove the load resistance of the circuit.
Step 2 :Find the internal resistance Rint of the source network by deactivating the constant sources.
Step 3: Now short the load terminals and find the short circuit current ISC flowing through the shorted load terminals using conventional network analysis methods.
Step 4: Norton’s equivalent circuit is drawn by keeping the internal resistance Rint in parallel with the short circuit current ISC.
Step 5: Reconnect the load resistance RL of the circuit across the load terminals and find the current through it known as load current IL.
What is Norton's Theorem
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