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.
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.
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.
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.
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
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.
Now find the equivalent resistance of this circuit looking
through the open circuited terminals a and b. This equivalent resistance will be the RTh .
Step-3 :- Find
Thevenin’s equivalent circuit.
Connect VTh ,Rth and 3Ω resistor , all in series , to get Thevenin’s equivalent circuit as
shown.
Step-4 :- Find current
through load resistor .
Current through 3Ω resistor can be easily
calculated as
