Norton’s theorem is a circuit analysis technique which is used to reduce complex electrical circuits to a single current source and one parallel resistor. Statement of Norton theorem:

**Any linear bilateral network can be reduced to a simple circuit containing one current source and one shunt resistor**

Given below are steps for Norton’s Theorem

- Replace all current zeros with open and all voltage sources with short
- Identify and remove the load from the circuit
- Label resulting terminals (We’ll label them x and y)
- Find the equivalent resistance
- Now again connect all sources
- Form a short circuit by connecting x and y
- Find current that flows through the circuit
- Connect current source (value obtained from step 6) to the shunt resistor (value obtained from step 4)

**Example**

Let’s solve an example for better understanding the Norton’s theorem

Consider the circuit given below:

Problem statement: Replace the circuit by Norton equivalent circuit for load resistor of 15 ohms.

Step 1: First of all zero all sources. i.e Replace voltage source by short and current source by open.

Step 2: Remove the load resistor

Step 3: Label the resulting terminals as x and y

Step 4: Find equivalent resistance

*Figure below illustrates step 1, 2, 3, and 4*

Here the equivalent resistance is 10 ohms

Step 5: Now again connect all sources to circuit:

Step 6: Short the terminals x and y

Step 7: Find the current flowing through short circuit

Since we have a circuit with multiple sources Superposition principle ideally suits the condition

Firstly replace current source and find current flowing through resistor:

Now replace voltage source by short and apply current divider to find current through resistor

Since we have a short circuit the overall current will flow through the short

The overall current flowing through short is:

**I (t) = I (1) + I (2) = 1.2 + 2.5 = 3.7 A**

Step 8: Using Req from 4 and current from 7th step we obtain equivalent circuit as follows: