Question

What is the state of Norton's theorem?

Answer 1

Norton's Theorem is a method used in electrical circuit analysis to simplify a complex linear circuit with respect to a particular load. The theorem states that any linear electrical network with voltage and current sources, as well as resistors, can be replaced by an equivalent circuit consisting of a current source in parallel with a resistor. This simplified equivalent makes it easier to analyze and solve circuits.

Here’s a breakdown of the state of Norton’s Theorem:

Components of Norton’s Equivalent Circuit:

1. Norton Current (Iₙ): This is the current that flows through the load when the load is disconnected from the network. It is the current provided by the equivalent current source.
   

   

1. Norton Resistance (Rₙ): This is the resistance seen by the load when all independent sources in the network are turned off (replaced by their internal resistances—voltage sources by short circuits and current sources by open circuits).
   

Steps to Find the Norton Equivalent:

1. Remove the Load Resistor from the circuit.
   

1. Find the Norton Current (Iₙ): This is the current that would flow through the open terminals (where the load resistor was) if the network were connected to an external load.
   

1. Find the Norton Resistance (Rₙ): This is the equivalent resistance of the network seen from the terminals where the load resistor was placed, with all independent sources turned off.
   

1. Construct the Norton Equivalent Circuit: Finally, represent the circuit as a current source (Iₙ) in parallel with the Norton resistance (Rₙ), and reconnect the load resistor.
   

Comparison with Thevenin’s Theorem:

1. Thevenin’s Theorem replaces the network with a voltage source and a series resistance.
   

1. Norton’s Theorem replaces the network with a current source and a parallel resistance.
   

1. Both theorems are related: Thevenin’s voltage can be converted into Norton’s current using the formula:  
   

  \[ Iₙ = \frac{V_{th}}{R_{th}} \]
  Where \(V_{th}\) is Thevenin’s equivalent voltage and \(R_{th}\) is Thevenin’s equivalent resistance.

In practice, Norton’s Theorem is helpful because it simplifies circuit analysis, especially when solving for current through or voltage across a load resistor.