Thévenin’s theorem

Thévenin’s theorem is an electrical network analysis theorem or technique developed by the German scientist Hermann von Helmholtz and French engineer Léon Charles Thévenin , and states that:

Any network or combination of sources and resistors with two terminals can be replaced by the equivalent circuit with a voltage source and a resistor in series. Where the voltage source of equivalent circuit is open circuit voltage at the terminals , and the resistance of the series resistor  of equivalent circuit is the value obtained by dividing the equivalent voltage source by the short circuit current on the terminals.

Using Thévenin’s theorem we can easily calculate the branch responses on a certain branch of a complex electrical network.

Thévenin’s Theorem

 


Thevenin Equivalent

Thevenin equivalent circuit is the equivalent circuit of a complex network with the Thevenin voltage source and Thevenin resistor in series of the Thevenin voltage source and the load.The process of finding the Thevenin equivalent is also sometimes called Thevenization of a circuit and the Thevenin equivalent circuit is called Thevenized circuit.

Thevenin Voltage

Thevenin equivalent voltage is the output voltage in the terminals of the network , when the terminal is open or without any load resistor. It is denoted by V_{th}.

Thevenin Resistance

Thevenin equivalent resistance is the resistance measured through the two points of the terminal after all internal voltage sources are replaced with a short and all internal current sources are replaced with an open.

Thevenin resistance can also be calculated mathematically by dividing the Thevenin voltage by the current flowing through the terminals with a short between terminals ; this particular mathematical technique can specially be used to calculate Thevenin resistance when the circuit contains dependent sources.

 It is denoted by V_{th}.

For Example consider the following circuit:

Thévenin’s theorem

The Thevenin equivalent of the above circuit is:

Thévenin’s theorem

Where,

V_{th} = V_{AB} = the voltage measured through the terminals A and B in the first circuit.

and  R_{th} = R_2 + \dfrac{1}{\frac{1}{R_1} + \frac{1}{R_3}} = The Resistance measured through the terminal A and B in the first circuit after the voltage source is replaced by a short.

 

Thévenin’s theorem example:

Using Thévenin’s theorem let us find the voltage drop and current through the 10 Ohms resistor in the following circuit:

Finding the V_{th}:

V_{th} = V_{AB} = Voltage at 8 Ohms resistor – 12 V

Finding Voltage at 8 Ohms resistor , using voltage divider formula: \dfrac{2}{2+5} \times 20 = 5.71 V

Thus ,  V_{th} = V_{AB} =5.71 – 12 = -6.29 V

Now finding  R_{th}:

R_{th}=R_{AB}=8\Omega +\dfrac{1}{\frac{1}{5}+\frac{1}{2}}\Omega =9.43\Omega

Thus the Thevenin Equivalent of the given circuit is:

Thus the Voltage drop Through 10 Ohms resistor = 3.24 Voltage , and the Current flowing through it = 0.32 Amps