Thevenin’s Theorem Solved example step-by-step


Thevenin’s  theorem is used to determine current through or voltage across any element in a network without going through the regorous method of solving a set of network equations.

Thevenin’s  Theorem statement

Any two terminal bilateral linear dc circuit can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.


Explanation :-
Consider the network enclosed in a box with two terminals A and B brought out as shown.

Thevenin’s  theorem explanation



The network in the box may consist of any number of resistors and voltage sources connected in any manner. 

But according to Thevenin , the entire circuit behind terminals A and B can be replaced by a single source of emf VTh (called Thevenin’s voltage) in series with a single resistance RTh (called Thevenin’s resistance) as shown in second figure. The procedure to find VTh and RTh  is discussed below. 
Once Thevenin’s equivalent circuit is obtained , current through the load RL across terminals A and B can be found out by ohm’s law as shown.
Thevenin’s  theorem
Lets solve an example step-by-step to understand the theorem better.


Thevenin’s theorem solved example

Find the current in 3Ω  resistor using Thevenin’s theorem.

Thevenin theorem solved example

The Thevenin’s theorem has four steps.

Step-1 :-  Find VTh

To find Thevenin’s voltage VTh  , remove 3Ω  resistor leaving other parts of the circuit as it is and calculate the voltage across the open circuited terminals a-b.

Thevenin theorem solved example


To find voltage across the open circuited terminals a-b lets assume potential at point c to be zero. Then potential at point b is equal to 10V .
In left side loop, by Kirchoff’s voltage law

20- 2I1- 5I1- I1- 5 =0 

Thevenin theorem solved example

Step-2 :-  Find RTh

Remove 3Ω  resistor and replace all independent voltage sources by short circuits (as internal resistance of ideal voltage source is zero) and all independent current sources by open circuits (as internal resistance of ideal current source is infinite) . 

Leave dependent voltage and current sources as it is. We will obtain a circuit with only resistances  and/or  dependent voltage and current sources as shown.

Thevenin resistance

Now find the equivalent resistance of this circuit looking through the open circuited terminals a and b. This equivalent resistance  will be the RTh .
Thevenin resistance

Step-3 :-   Find Thevenin’s equivalent circuit.

Connect VTh ,Rth and 3Ω resistor , all in series , to get  Thevenin’s equivalent circuit as shown.

Thevenin equivalent circuit


Step-4 :-  Find current through load resistor .

Current through 3Ω resistor can be easily calculated as 

Thevenin theorem solved example



Closely related concepts :-
  (1) Methods of finding Thevenin Resistance