Thevenin’s Theorem
Thevenin’s theorem was named after a French
engineer M. L Thevenin (1857 -1926) who while working in the telegraphic
department published a statement of the theorem in 1893. The theorem provides a
mathematical technique for replacing a given network as viewed from two output
terminals, by a single voltage source with a series resistance. It makes the
solution of complicated resistance. It makes the solution of complicated
networks (particularly, electronic networks) quite quick and easy. The
application of this powerful theorem will be explained with the help of the
following simple example
engineer M. L Thevenin (1857 -1926) who while working in the telegraphic
department published a statement of the theorem in 1893. The theorem provides a
mathematical technique for replacing a given network as viewed from two output
terminals, by a single voltage source with a series resistance. It makes the
solution of complicated resistance. It makes the solution of complicated
networks (particularly, electronic networks) quite quick and easy. The
application of this powerful theorem will be explained with the help of the
following simple example
Suppose we are required to find the current flowing
through the load resistance RL in figure 1a above, we can use
Thevenins’ theorem and proceed as:
through the load resistance RL in figure 1a above, we can use
Thevenins’ theorem and proceed as:
1.
Disconnect RL from the circuit terminals A and B and redraw
the circuit as shown in figure 1b. Obviously, the terminals have become open
circuited.
Disconnect RL from the circuit terminals A and B and redraw
the circuit as shown in figure 1b. Obviously, the terminals have become open
circuited.
2.
Calculate the open circuit voltage (VOC) which appears across
terminals A and B when they are open i.e when RL is disconnected.
Calculate the open circuit voltage (VOC) which appears across
terminals A and B when they are open i.e when RL is disconnected.
as seen,
VOC = drop across R2 = IR2 where I is the
circuit current when A and B are open
VOC = drop across R2 = IR2 where I is the
circuit current when A and B are open
From the above expressions, it is clear that any
network of resistors and voltage sources (and current sources as well) when
viewed from any two point A and B in the network, can be replaced by a single
voltage source and a single resistance ( or impedance in the case of a.c
circuits) in series with the voltage source.
network of resistors and voltage sources (and current sources as well) when
viewed from any two point A and B in the network, can be replaced by a single
voltage source and a single resistance ( or impedance in the case of a.c
circuits) in series with the voltage source.
After this replacement of the network by a single
voltage source with a series resistance has been accomplished. It is easy to
find current in any bad resistance joined across terminals A and B. This
theorem is valid even for those linear networks which have a non-linear load.
voltage source with a series resistance has been accomplished. It is easy to
find current in any bad resistance joined across terminals A and B. This
theorem is valid even for those linear networks which have a non-linear load.
Therefore Thevenin’s theorem as applied to d.c
circuit can be stated as:
circuit can be stated as:
The current flowing through a load resistance
connected across any two terminals A and B of a linear, active bilateral
network is given by Voc/ (Rth + RL) where Voc
is the open circuit voltage (i.e. voltage across the two terminals when RL
is removed) and Rth is the internal resistance of the network as
viewed back into the open circuited network from terminals A and B with all
voltage source replaced by their internal resistance( if any) and current
source by infinite resistance.
connected across any two terminals A and B of a linear, active bilateral
network is given by Voc/ (Rth + RL) where Voc
is the open circuit voltage (i.e. voltage across the two terminals when RL
is removed) and Rth is the internal resistance of the network as
viewed back into the open circuited network from terminals A and B with all
voltage source replaced by their internal resistance( if any) and current
source by infinite resistance.
