Thevenin’s Theorem
For the following Circuit, determine the Thevenin Voltage
and the Thevenin Resistance. Create a Thevenin Model
then test three resistors for a load resistor to determine
which one transfers maximum power from the source to the
load.
Thevenize the circuit at points A and B. Step 1: Remove the load
resistor and determine the open circuit voltage at those nodes. [No
current flows through the two 2K ohm resistors so they are not part
of the voltage solution. The 1K ohm resistor in parallel with the
source does not reduce the voltage at the output terminals and is
therefore not involved in the solution. The remaining three
resistors form a voltage divider across the source. The voltage of
interest, is the voltage across the 4K ohm resistor.]
V AB =
4K
xV T
1K + 4K + 3K
V AB =
4K
1
x16 = x16 = 8Volts
8K
2
The Thevenin Voltage is 8 volts.
Step 2 is to determine the resistance looking into the circuit from the point of view of
terminals A and B. The Sources will be replaced with their internal resistance for this
C:\_ghw\Courses\ElecCir\Thevenin_revisit.doc
gwalsh@northshore.edu
step. The voltage source with therefore be replaced with a short circuit, a wire. The
resulting resistor network can be reduced as shown:
The three series resistors add up to 6K ohms and is the Thevenin resistor.
The model is complete as shown:
Trial and error exercises can now be
calculated using the model in place
the original circuit. The results for
the load with be the same for the
Thevenin Circuits as they would for
the original circuit.
of
Test three load resistors and
determine which one results in the maximum power delivered to the load. Connect the
first to the model, determine total resistance, and total current, then calculate power
dissipated by the load resistor. Repeat for the other two resistors.
C:\_ghw\Courses\ElecCir\Thevenin_revisit.doc
gwalsh@northshore.edu
RT = RTH + RL
IT =
VTH
RT
PRL = I T RL
2
The table shows the results of calculations. The maximum power delivered to the load is
when the load resistor is 6K ohms. The value matches the Thevenin resistor and proves
the maximum power transfer theorem. The maximum power is transferred to the load
when the load resistor is equal to the source resistance.
RL
5K
6K
7K
RT
11K
12K
13K
IT
.727mA
.666mA
.615mA
PRL
2.64mW
2.66mW
2.65mW
The curve for this data show the power peaking when RL=6K ohms:
C:\_ghw\Courses\ElecCir\Thevenin_revisit.doc
gwalsh@northshore.edu