# What is Norton's Theorem?

**Norton’s theorem**is just like Thevenin’s theorem. It is a theorem of transforming a complex linear circuit into a simple circuit. This theorem states that any two-terminal linear network or circuit containing energy sources and resistances can be replaced by an equivalent circuit containing a single current source IN in parallel with a resistance RN.

Where IN is the short circuit current (called

**Norton's current**) at the terminals to which the load resistance is connected and RN is the resistance (called**Norton's resistance**) measured between the terminals with all energy sources are replaced by their internal resistances.Here the simple circuit which is transformed from the complex circuit is known as

**Norton's equivalent circuit**. However, there are some methods to find this Norton's equivalent circuit which we will know below. Before that let us know a little bit about the constant current source first.What is a Constant Current source?

**A constant current source**delivers energy to a circuit such that the current drawn from the source is independent of the voltage across the terminals.

Let us consider a voltage source of emf E and internal resistance Ri supplying power to a load resistance RL.

The load current,

The voltage at the terminals of the voltage source

If RL is varied, I remain constant although the terminal voltage Vt changes. Thus a voltage source behaves as a constant current source when its internal resistance is much larger than the load resistance. For an ideal current source, the internal resistance is infinite.

## Norton's equivalent circuit

To find Norton's equivalent circuit or simplifying any linear circuits we consider a circuit with a complicated linear network driven by an energy source (VS). Where the network also contains three resistors (R1, R2, and R3) and they are connected with a load (RL).

After Norton's conversion, this complicated linear network exactly looks like this...

Where the circuit contains just a single current source and parallel resistance connected to a load.

## Steps to remember to find out Norton’s Equivalent Circuit

• Identify the load resistance (RL).

• Replace the load with a short circuit and calculate the current (called Norton's current IN) through the short circuit.

• Replace the energy source with their internal resistances and calculate the resistance (called Norton's resistance RN) across the open ends.

## Solved problems by Norton's Theorem

__Problem no - 1__: Calculate the current through the resistance 4Ω by applying Norton's Theorem.

__Solution:__

**Identify the load resistance (RL):**

Here the load resistance is 4Ω.

**Find the Norton Current (IN):**

Now replace the load with a short circuit and calculate the current (called Norton's current IN) through the short circuit.

By applying Kirchhoff's Voltage Law (KVL) in loop 1, we get

By applying Kirchhoff's Voltage Law (KVL) in loop 2, we get

Using equation no - (2) in equation no - (1), we get

**Find the Norton Resistance (RN):**

Now replace the energy source with their internal resistances and calculate the resistance (called Norton's resistance RN) across the open ends.

Here,

**Norton's equivalent circuit**

We connect the load resistance RL across the current source IN (Norton's current) shunted by the resistance RN.

Now the voltage across the RN and RL in parallel is

Therefore, the current through the load resistance RL is given by

__Problem no - 2__: **Calculate the current through the resistance R****L**** = 5**Ω** by applying Norton's Theorem.**__Solution:__

**Identify the load resistance (RL):**

Here the load resistance is 5Ω.

**Find the Norton Current (IN):**

Now replace the load with a short circuit and calculate the current (called Norton's current IN) through the short circuit.

By applying Kirchhoff's Voltage Law (KVL) in loop 1, we get

__Problem no - 1__: Calculate the current through the resistance 4Ω by applying Norton's Theorem.

__Solution:__**Identify the load resistance (RL):**

**Find the Norton Current (IN):**

**Find the Norton Resistance (RN):**

**Norton's equivalent circuit**

__Problem no - 2__:**Calculate the current through the resistance R**

**L**

**= 5**Ω

**by applying Norton's Theorem.**

__Solution:__

**Identify the load resistance (RL):**

Here the load resistance is 5Ω.

**Find the Norton Current (IN):**

By applying

**Kirchhoff's Voltage Law (KVL)**in loop 2, we getUsing equation no - (2) in equation no - (1), we get

**Find the Norton Resistance (RN):**

Now replace the energy source with their internal resistances and calculate the resistance (called Norton's resistance RN) across the open ends.

Here,

**Find the Norton Resistance (RN):**

**Norton's equivalent circuit**

## We connect the load resistance RL across the current source IN (Norton's current) shunted by the resistance RN.

Here RN and RL in parallel, so the equivalent resistance

Now the voltage across the RN and RL in parallel is

Therefore, the current through the load resistance RL is given by