# Nortons Theorem

Nortons theorem is an analytical method used to change a complex circuit into a simple equivalent circuit consisting of a single resistance in parallel with a current source**Nortons Theorem**states that “

*Any linear circuit containing several energy sources and resistances can be replaced by a single Constant Current generator in parallel with a Single Resistor*“.

As far as the load resistance, R

_{L}is concerned this single resistance, R

_{S}is the value of the resistance looking back into the network with all the current sources open circuited and I

_{S}is the short circuit current at the output terminals as shown below.

### Nortons equivalent circuit

For example, consider our now familiar circuit from the previous section.

When the terminals A and B are shorted together the two resistors are connected in parallel across their two respective voltage sources and the currents flowing through each resistor as well as the total short circuit current can now be calculated as:

### with A-B Shorted Out

### Find the Equivalent Resistance (Rs)

### Nortons equivalent circuit

Ok, so far so good, but we now have to solve with the original 40Ω load resistor connected across terminals A and B as shown below.Again, the two resistors are connected in parallel across the terminals A and B which gives us a total resistance of:

The voltage across the terminals A and B with the load resistor connected is given as:

Then the current flowing in the 40Ω load resistor can be found as:

which again, is the same value of 0.286 amps, we found using Kirchhoff´s circuit law in the previous tutorials.

## Nortons Theorem Summary

The basic procedure for solving a circuit using**Nortons Theorem**is as follows:

**1.**Remove the load resistor R_{L}or component concerned.**2.**Find R_{S}by shorting all voltage sources or by open circuiting all the current sources.**3.**Find I_{S}by placing a shorting link on the output terminals A and B.**4.**Find the current flowing through the load resistor R_{L}.