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University of Sharjah
Electrical and Electronics Engineering Department
0402203
Circuit Analysis I Laboratory
Experiment # 5
Thevenin’s and Norton’s Equivalents of DC Circuits
OBJECTIVE:
To understand and verify the Thevenin's and Norton's Theorems by the use of DC circuits.
PRE-LAB:
1. Find and draw the Thevenin’s and Norton’s equivalents of the circuit shown in Fig 2.
2. Find VL, IL and PL for the values of RL shown in Table 2.
3. Plot PL versus RL. From this plot, find RL that absorbs the maximum power from the circuit and
find the value of this maximum power (Pmax).
4. Plot VL versus IL. This plot should be a straight line, find the slope, y-intercept and the equation of
this straight line.
THEORY:
Any electrical network containing sources and circuit elements can be represented (or replaced), at any
given pair of terminals, by a model (equivalent circuit) containing a single ideal source and a single
element. The Thevenin's Model is an ideal voltage source in series with a resistor; and Norton's Model
is an ideal current source in parallel with a resistor. Figure 1 shows the Thevenin's and Norton's models
for DC networks.
Figure 1: a) Thevenin Equivalent Circuit
b) Norton Equivalent Circuit
The Thevenin’s Model represents the network with its open-circuit voltage, VOC, and internal
resistance, RTH, whereas the Norton Model represents the network with its short-circuit current, ISC, and
internal resistance, RTH. The parameters of these models can be calculated or measured, depending on
the complexity of the given network.
The parameters for Thevenin's equivalent, Voc and RTH, may be obtained experimentally by following
steps
1. Remove the load from the terminals of the network between which you want to find the equivalent
circuit.
2. Measure the voltage across the two terminals, this is Voc.
3. Use the multimeter to measure the resistance between the two terminals with all independent
voltage sources replaced with short-circuits and all independent current-sources replaced with
open-circuits (can you find any current source in the lab !!).
4. Connect Voc and RTH in series to obtain the Thevenin's equivalent of the original circuit as shown
in Figure 1(a).
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The parameters for Norton’s equivalent, Isc and RTH, may be obtained experimentally by following
steps:
1. Short the terminals of the network between which you want to find the Norton's equivalent circuit.
2. Measure the current flowing between short-circuited terminals of the network, this is the Isc.
3. Use the multimeter to measure the resistance between the two terminals with all independent
voltage sources replaced with short-circuits and all independent current-sources replaced with
open-circuits.
4. Connect Isc and RTH in parallel as shown in Figure 1(b) to obtain the Norton's equivalent of the
original circuit. (since there is no current sources in the labs, Norton's equivalent circuit is only
mathematical model).
Maximum Power Transfer:
One application of the Thevenin's and Norton's Theorems is to enable us to find the value of the load
resistance that will draw the maximum possible power from the circuit. The maximum power transfer
theorem states “An independent voltage source (Voc) in series with a resistance (RTH) delivers
maximum power to the load resistance (RL) for which
RL=RTH and Pmax 
V 2 oc
4 RTH
PROCEDURE:
1.
2.
3.
4.
5.
Connect the circuit shown in Figure 1, with
RL removed (open circuit):
Measure Voc the open circuit voltage between
the nodes a and b. Record your results in
Table 1.
Measure Isc , the short circuit current from a
to b and record it Table 1.
Measure RTH, the equivalent resistance
between the nodes a and b.
Connect RL then measure VL and IL for the
values of RL listed in Table 2.
Figure 2
Table 1: Measurements for Thevenin’s and Norton’s Equivalents
Measured
Calculated
Open Circuit Voltage (VOC)
Short Circuit Current (ISC)
Equivalent Resistance (RTH)
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Table 2: Measurements of VL and IL for different values of RL
RL
VL
(measured)
VL
(calculated)
Percent
Error
IL
(measured)
IL
(calculated)
Percent
Error
PL
(measured)
PL
(calculated)
Percent
Error
0.0 kΩ
1.0 kΩ
1.5 kΩ
2.0 kΩ
2.5 kΩ
3.0 kΩ
3.5 kΩ
4.0 kΩ
4.5 kΩ
5.0 kΩ
Note the measured power is found from the measured voltage and current.
RESULTS:
1. From the measurements, draw the Thevenin’s and Norton’s equivalents of the given circuit. Then compare
them to the calculated circuits.
2. From the measurements, verify that Voc=RTH Isc .
3. Fill Table 2 with both the measured and the calculated values.
4. Plot PL versus RL (the measured values).
5. From this plot, find RL that absorbs the maximum power from the circuit and find the value of this maximum
power (Pmax). Then compare these results to the calculated values.
6. Plot VL versus IL (the measured values).
7. This plot should be a straight line, find the slope, y-intercept and the equation of this straight line.
8. Compare the slope and y-intercept with the Thevenin equivalent circuit. Compare both measured and
calculated results.
QUESTIONS:
Q 1. What is meant by the word " equivalent " in Thevenin's equivalent circuits?
Q 2. Thevenin's equivalent of a circuit can be obtained by calculating or measuring two values Voc
and Isc. Often, it is not practical to measure the short circuit current. Can you imagine trying to
measure the short circuit for a car battery (or any voltage source)? Suppose you wanted to obtain
the Thevenin's equivalent of a car battery by making two measurements, neither of which
involves measuring Isc. For example measure Voc and then place 2kΩ resistor across the
terminals and measure the voltage across the resistor. Do you have enough information from
these two measurements to obtain the Thevenin's Equivalent circuit? Justify your answer in
detail. Draw the Thevenin’s equivalent of such a circuit if VOC = 12V and V2k = 2V. [Hint: Take
help from parts 6,7 & 8 of results].
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