11Thevenin’s
Theorem
Objectives:
1. Change a linear network containing several resistors into an
equivalent thevenin circuit.
2. Prove the equivalency of the network in objective 1 with the
Thevenin circuit by comparing the effects of various resistors.
Summary of Theory:
Thevnin’s theorem provides a means of reducing a complicated,
linear network into an equivalent circuit when there are two
terminals of special interest (usually the output). The equivalent
thevenin circuit is composed of a voltage source and a series resistor.
(In ac circuits, the resistor may be represented by opposition to ac
called impedance). Two steps are required in order to simplify a
circuit to its equivalent thevenin circuit. The first step is to measure
or compute the voltage at the output terminals with any load
resistors removed. This open circuit voltage is the thevnenin voltage.
The second step is to compute the resistance seen at the same open
terminals if sources are replaced with their internal resistance. For
voltage sources, the internal resistance is infinite (open circuit)
Materials Needed:
Resistors: one 10 kΩ, one 2.2 kΩ, one 1kΩ.
One 1kΩ potentiometer.
Procedure:
1. Measure and record the resistance of the 6 resistors listed in
Table 12-1. The last three resistors will be used as load
resistors and connected, one at time, to the output
terminals.
Table 12-1
Component
R1
R2
R3
RL1
RL2
RL3
Listed value
10kΩ
1kΩ
2.2k Ω
1.6kΩ
4.7kΩ
8.2kΩ
Measured value
9.756kΩ
0.983kΩ
2.196kΩ
1.598kΩ
4.688kΩ
8.189kΩ
2. Construct the circuit shown in Figure 12-3. Points A and B
represent the output terminals. Calculate an equivalent
circuit seen by the voltage source. Figure 12-4 illustrates the
procedure. Use the equivalent circuit to compute the
expected voltage across the load resistor, VL1. Do not use
Thevenin’s theorem at this time. Show your computation of
the load voltage in the space provided. For the first load
resistor, your computed result should be approximately 1.19
V.
3. Measure the load voltage to verify your calculation. Enter
the computed and measured load voltage in Table 12-2.
VL1
VL2
VL3
VTH
RTH
Computed
0.656 V
1.138 V
1.336 V
1.803 V
2.803 KΩ
Measured
0.673 V
1.151 V
1.369 V
1.833 V
2.775 KΩ
4. Replace RL1 with RL2. Using a new equivalent circuit, compute
the expected voltage, VL1 , across the load resistor. Then
measure the actual load voltage. Enter the computed and
measured voltage in Table 12-2.
5. Repeat step 4 using RL3 for the load resistor.
6. Remove the load resistor from the circuit. Calculate the
open circuit voltage at the A-B terminals. This open circuit
voltage is the thevenin voltage for this circuit. Record the
open circuit voltage in Table 12-2 as VTH.
7. Mentally replace the voltage source with a short (zero
ohms). Compute the resistance between the A-B terminals.
This is the computed Thevenin resistance for this circuit.
Then disconnect the voltage source and replace it with a
jumper. Measure the actual thevenin resistance of the
circuit. Record you’re computed and measured thevenin
resistance in Table 12-2.
8. In the space provided, draw the Thevenin equivalent circuit.
Show on your drawing the measured Thevenin voltage and
resistance.
Table 12-3
VL1
VL2
VL3
VTH
RTH
Computed
0.0825 V
2.096 V
1.823 V
6.875 V
10.687 KΩ
Measured
0.075 V
1.953 V
1.752 V
6.907 V
10.434 KΩ
9. For the circuit you drew in step 8, compute the voltage you
expect across each of the three load resistors. Since the
circuit is a series circuit, the voltage divider rule will simplify
the calculation. Enter the computed voltages in Table 10-3.
Conclusion:
Thevnin’s theorem provides a means of reducing a complicated,
linear network into an equivalent circuit when there are two
terminals of special interest (usually the output).