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EXPERIMENT 3
THEVENIN’S THEOREM, NORTON’S THEOREM’S
AND MAXIMUM POWER TRANSFER
OBJECTIVE
1. Validate Thevenin’s theorem and Norton’s theorem through experimental
measurements.
2. Become aware of an experimental procedure to determine VTh, IN and RTh or RN.
Hence the Thevenin and Norton equivalent circuits.
3. Demonstrate the conditions for maximum power transfer to a load are RL = RTh and
VL = VTh/2.
INTRODUCTION
Through the use of Thevenin’s and Norton’s theorems, a complex two-terminal, linear,
multi-source dc circuit can be replaced by one simplified circuit having single source and
resistor looking into a pair of terminals of our interest . The Thevenin equivalent circuit
consists of an open-circuit dc voltage, VTh in series with an open-circuit resistance, RTh
(determined when all sources being removed from the circuit). While the Norton’s
equivalent circuit consists of a short-circuit dc current, IN in parallel with a single resistor,
RN defined exactly the same way as RTh.
x
Complex twoterminal, linear,
multi-source circuit
RL
y
(a)
Complex two-terminal,
linear, multi-source circuit
with all sources removed.
Voltage source - short
circuited.
current source - open
circuited.
(b)
x
Complex twoterminal, linear,
multi-source circuit
VTh
Complex twoterminal, linear,
multi-source circuit
y
(c)
x
RTh = RN
y
x
IN
y
(d)
Figure 3.1: (a) Original complex circuit seen from terminals x-y. (b) Defining RTh = RN
(c) Defining VTh (d) Defining IN
The equivalent circuits for Thevenin and Norton are depicted in Figure 3.2 below.
1
RTh
x
VTh
x
RL
(a)
RN
IN
(b)
y
RL
y
Figure 3.2: (a) Thevenin equivalent circuit (b) Norton equivalent circuit
The theory of source conversion dictates that the Norton and Thevenin circuits be
terminally equivalent and related as follows:
RN  RTh
VTh  I N RN
and
IN 
VTh
RTh
(3.1)
If a dc voltage source is to deliver maximum power to a resistive load, the load resistor
RL must have a value equal to the Thevenin equivalent resistance, RTh “seen” by the load.
For this value, the voltage across the load will be one-half of the Thevenin voltage. In
mathematical expression,
RL  RTh ,
V
VL  Th
2
2
and
Pmax
V
 Th
4 RTh
(3.2)
EQUIPMENT/COMPONENT
Multimeter (1)
Variable DC Power Supply (1)
Resistor (1/4 W) – 3.3 k, 1 k , 2.2 k, 470 
Breadboard (1)
Alligator clip wire (2)
**For all theoretical calculation results students are strictly required to show their work
in progress (formula form/complete figures) in the PRE-LAB space provided before the
lab session. Otherwise they will be forbidden from participating the session. There will
be certain marks allocated for this part.
PROCEDURE
PART 1: THEVENIN’S THEOREM AND NORTON’S THEOREM
1. Construct the circuit as depicted in Figure 3.3. Insert the measured resistance values
in Table 1.
2
3.3 k
R1
Vs
12 V
x
1 k
R3
R2
2.2 k
IL
+
VL
-
RL = 470 
y
Figure 3.3: Circuit diagram for Thevenin’s and Norton’s theorems application
2. Turn on the supply and measure the voltage VL. Using ammeter or from Ohm’s law,
calculate the current IL. Insert the results in Table 2.
Determining RTh / RN:
3. Determine RTh / RN by replacing the voltage source with a short-circuit equivalent and
measuring the resistance with ohmmeter between terminal x-y with RL being removed
as depicted in Figure 3.4.
3.3 k
1 k
R1
Vs
x
R3
R2
m
2.2 k
y
Figure 3.4: Determining Rth / RN
Determining VTh:
4. Determine VTh by constructing the circuit of Figure 3.5 and measuring the opencircuit voltage between terminal x-y with voltmeter. Insert all results in Table 2.
3.3 k
1 k
R1
Vs
x
R3
R2
2.2 k
Vm
y
Figure 3.5: Circuit connection for determining Vth
3
Determining IN:
5. Determine IN by constructing the circuit depicted in Figure 3.6 and measuring the
short circuit current between terminal x-y with ammeter. Insert the result in Table 2.
3.3 k
x
1 k
R1
R3
R2
Vs
Am
2.2 k
y
Figure 3.6: Circuit connection for determining IN
Thevenin Equivalent Circuit:
6. Construct the Thevenin equivalent circuit as depicted in Figure 3.7 using values
obtained in parts 3 and 4 respectively. Use ohmmeter to set the potentiometer
properly. Then measure the voltage VL and IL. Insert the values in Table 2.
7.
0 - 10 k
x
VTh
R1
IL
+
VL
-
RL = 470 
y
Figure 3.7: Constructing Thevenin equivalent circuit
PART 2: MAXIMUM POWER TRANSFER
1. Replace RL in Figure 3.3 with a 10-k potentiometer without disturbing the previous
position of the wiper arm. Measure the load voltage VL across the potentiometer to
check the conditions that at RL = RTh, the load voltage is half the amount of the
Thevenin voltage. Record your observation in Table 3.
4
3.3 k
1 k
R1
Vs
12 V
x
R3
R2
RL = 0 - 10k
2.2 k
IL
y
Figure 3.8: Determining Rth / RN
2. Leave the potentiometer as connected in Figure 3.8 and measure VL for all values of
RL appearing in Table 4. Then calculate the resulting power to the load and complete
the table. At the very least, remember to disconnect one side of the potentiometer
when making the setting.
5
Name: ________________________________ Matrix No: ______________ Date: _________
________
RESULT
Resistor
Designation
Measured Value ()
R1
R2
R3
RL
Table 1: Measured resistors values.
Param.
Theoretical Result
(PRE-LAB)
Experimental
Result
Original
Circuit
Thevenin/
Norton
Circuit
Percentage
Difference (%)
Original
Circuit
Thevenin/
Norton
VTh (V)
RTh / RN
(k)
IN (mA)
VL(V)
IL (mA)
Table 2: Thevenin and Norton electrical parameters, voltage and load current.
Load Voltage, VL
(Volt)
Load Resistance, RL
(Ohms)
Table 3: Conditions for maximum power transfer to the load.
Instructor Approval: _________________________________
6
Date: ______________
Name: ________________________________ Matrix No: ______________ Date: _________
________
RL
VL (measured)
(Volt)
PL = VL2 / RL (calculated)
(miliWatt)
400 
800 
1.2 k
1.6 k
2 k
2.4 k
2.8 k
3.2 k
Table 4: Experimental results to re-confirm the conditions for maximum power transfer
to the load.
Instructor Approval: _________________________________
7
Date: ______________
Name: ________________________________ Matrix No: ______________ Date: _________
________
PRE-LAB CALCULATION (Show your WIP)
(All calculations should be done in rms values)
(a) Calculate the Thevenin voltage, Norton current and equivalent resistance for the
circuit in Figure 3.3 to the left of terminal x-y using the measured resistor values.
Insert the calculated values in Table 2.
Answer:
VTh:
RTh / RN:
IN:
(b) Draw the Thevenin and Norton equivalent circuit for part (a) and calculate the load
voltage VL and current IL.
Answer:
Schematic Diagram:
Thevenin equivalent Cct:
Norton equivalent Cct:
VL = _________
IL = _________
VL= ___________
IL = ___________
Instructor Approval: _________________________________
8
Date: ______________
Name: ________________________________ Matrix No: ______________ Date: _________
________
(c) Calculate IL and VL in the original circuit of Figure 3.3 using series-parallel
techniques (use measured resistor values).How do these calculated values compare to
the one obtained in part (b)? (Just to check that Thevenin/Norton is valid simplifying
theorems)
Answer:
IL:
Instructor Approval: _________________________________
9
Date: ______________
Name: ________________________________ Matrix No: ______________ Date: _________
________
EVALUATION QUESTION
1. In this experiment noting the overall results in Table 2, have Thevenin’s theorem and
Norton’s theorem been verified?
Answer:
_____________________________________________________________________
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2. Reviewing Table 4, what is the range of the load resistance RL and voltage VL that
you think the maximum power may take place if you are to plot the graph of PL and
VL versus RL.
Answer:
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3. What effect would you think increasing RL have on voltage across R3?
Answer:
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
4. As homework exercise, study the circuit in Figure E1 below.
6 k
x
8 mA
4 k
2 k
V = 36 V
y
Figure E1: Circuit for problem 4
(a) Determine RTh and VTh for the network external to the 2-k resistor.
Instructor Approval: _________________________________
10
Date: ______________
Name: ________________________________ Matrix No: ______________ Date: _________
________
(b) Determine power delivered to the 2-k resistor using the Thevenin equivalent
circuit.
(c) Is the power determined in pat (b) the maximum power that could be delivered to
a resistor between terminals x and y? If not, what is the maximum power?
Instructor Approval: _________________________________
11
Date: ______________