Thevenin's theorem : Concept and Numericals.

Thevenin's theorem states that a linear and bilateral electrical network as seen from a load terminal is equivalent to a circuit having a voltage source Voc and series resistance Rin.

Where,

Voc is open circuit voltage also called thevenin voltage(Vth) is voltage across the load terminal after load has been removed from the network.

Rin is the internal resistance of the network as seen from the load terminal after the load has been removed from the network and all voltage sources replaced by their internal resistance (short circuited if internal resistance not provided) and current sources open circuited. It is also called thevenin resistance Rth.

For example:

Let the given below circuit has to find Thevenin voltage (Vth) and Thevenin resistance (Rth) across R(L).

Finding Thevenin voltage, Vth:

(i)   Open circuit the terminal AB

(ii)  Use network analysis method or a voltmeter to find Thevenin voltage, Vth.

In Figure

This voltmeter reading gives the Thevenin voltage Vth or open circuit voltage.

Finding the thevenin resistance:-

(i)   Replace voltage source with its internal resistance if given otherwise short circuit it.

(ii)  Replace current source with open circuit.

(iii) Calculate Thevenin resistance, Rth.

Or,

(i) Use Ohmmeter.

In Figure,

Thevenin Equivalent Circuit:-

Finding Current flowing through the load:-

Current flowing through the load, I(L) = Vth / (Rth + R(L))

Numericals:-

1.

Determine Vth, Rth and the current through 5KΩ resistor using Thevenin's theorem.

Solution:

(i)  Open circuit the 5 KΩ resistor. Now the circuit becomes as given below

Finding Thevenin voltage, Vth

Vth = 48 V * 4K/(4K + 12K) = 48 V * 4K/16K

       = 48V/4 

       = 12 V

Here the Thevenin voltage Vth is found to be 12 V.

(ii)  Short circuit the 48V voltage source. Now the circuit looks like:

Finding Thevenin resistance, Rth

Here 12K and 4K are in parallel and in series with 8K resistor.

So, Rth = 8K + (12K ∥ 4K)

            = 8K + ( 12 *4)K / (12+4)

            = 8K + 3K

            = 11K

Here Thevenin resistance is found to be 11KΩ.

Thevenin equivalent circuit can be drawn as follows:-

To find the current flowing through 5 KΩ, connect the 5 KΩ resistor to the Thevenin's equivalent circuit open terminal as follows:

Current flowing through the 5 KΩ resistor 

= 12V / (11KΩ + 5KΩ)

= 12V/16KΩ

= 0.75 mA

Values are found to be as below:-

Vth = 12V

Rth = 11 KΩ

Current flowing through the 5 KΩ resistor = 0.75 mA .