## Thevenin theorem and Norton theorem | thevenin vs Norton

This page covers basic description of thevenin theorem and Norton theorem. It mentions step by step guide to solve the network using thevenin theorem and Norton theorem.

Both of these are used widely as network theorems. It is useful where is is needed to find current through or voltage across any element of a network without solving any complex equations.

### Thevenin Theorem

As per **thevenin theorem**, "any two terminal bilateral linear DC circuit can be replaced by an equivalent circuit consisting of a
voltage source and a series resistor.

Let us take example as mentioned in figure-1 and derive I_{L} using thevenin theorem.

1. Find V_{oc} ,

First r_{L} is removed and then V_{oc} is found using following equation.

⇒V_{oc} = I*r3 = [ Vs/(r1+r3) ]* r3

2. Find R_{th}

Determine thevenin resistance of the circuit by replacing voltage source by short circuit.
If current source is present in the network, replace it by open circuit.

3. Find I_{L} as mentioned in thevenin equivalent circuit shown in Fig.1(d)

⇒I_{L} = [ V_{oc}/(R_{Th} + r_{L} ) ]

Thevenin network ≡ equivalent voltage source in series with internal resistance.

### Norton Theorem

**Norton theorem** is converse of the Thevenin theorem mentioned above.
It consists of equivalent current source instead of equivalent voltage source as used in thevenin theorem.

The similarity between the two is that calculation of internal resistance of the network is same.

Norton network ≡ equivalent current source in parallel with internal resistance

Following steps are used to determine Norton equivalent circuit.

1. Find I_{SC}

In order to determine I_{SC}, replace r_{L} by short circuit.

⇒ i = Vs/[ r1 + {(r2*r3)/(r2+r3)} ] and I_{SC} = i *[ r3/(r3+r2)]

2. Find R_{TH}

Now remove the short circuit and deactivate independent source to determine R_{int} as follows

⇒ R_{int} = r2 + [(r1*r3)/(r1+r3)]

3.
As per Norton theorem, the equivalent source circuit would contain current source in parallel with internal resistance.
Current source will be short circuited current across shorted terminals of the load resistor.

⇒ I_{L} = i_{SC} * [ R_{int}/R_{int} + r_{L} ]

### Electronic Components Related Links

Variable capacitor Variable resistor Transformer basics and types Ohm law Electrolytic capacitor Capacitor basics Inductor basics Relay Reed Switch SCR or thyristor Op-Amp

### What is Difference between

BJT vs FET Diac vs Triac JUGFET vs MOSFET LED vs Laser Photo Diode vs Photo Transistor