EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
UNIVERSITY MALAYSIA PERLIS
EKT 101
ELECTRIC CIRCUIT THEORY
LAB 4
SEMESTER I (2016/2017)
SCHOOL OF COMPUTER AND COMMUNICATION ENGINEERING
NAME
: ______________________________________
MATRIX NO
: ______________________________________
PROGRAMME
: ______________________________________
DATE
: ______________________________________
LECTURER’S NAME
: ______________________________________
1
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
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)
(b)
x
Complex twoterminal, linear,
multi-source circuit
VTh
x
Complex two-terminal,
linear, multi-source circuit
with all sources removed.
Voltage source - short
circuited.
current source - open
circuited.
Complex twoterminal, linear,
multi-source circuit
y
RTh = RN
y
x
IN
y
(d)
(c)
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.
RTh
x
VTh
x
RL
(a)
y
RN
IN
(b)
RL
y
Figure 3.2: (a) Thevenin equivalent circuit (b) Norton equivalent circuit
2
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
The theory of source conversion dictates that the Norton and Thevenin circuits be terminally
equivalent and related as follows:
R N  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,
R L  RTh ,
2
V
V L  Th
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.
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.
3
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
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.
x
3.3 k
1 k
R1
R3
Vs
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 open-circuit voltage
between terminal x-y with voltmeter. Insert all results in Table 2.
x
3.3 k
1 k
R1
R3
R2
Vs
Vm
2.2 k
y
Figure 3.5: Circuit connection for determining Vth
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
1 k
R1
R3
R2
Vs
x
2.2 k
Am
y
Figure 3.6: Circuit connection for determining IN
4
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
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
R1
VTh
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.
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
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
RESULT
Resistor
Designation
Measured Value ()
R1
R2
R3
RL
Table 1: Measured resistors values.
Param.
Experimental
Result
Original
Thevenin/
Circuit
Norton
Circuit
Theoretical Result
(PRE-LAB)
Percentage
Difference (%)
Original
Thevenin
Circuit
/
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.
6
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
RL
LABORATORY MODULE
VL (measured)
(Volt)
PL = VL2 / RL (calculated)
(miliWatt)
400 
800 
1.2 k
1.6 k
2 k
2.4 k
.8 k
3.2 k
Table 4: Experimental results to re-confirm the conditions for maximum power transfer to the load.
7
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
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 = ___________
(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:
8
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer
EKT101/4 ELECTRIC CIRCUIT THEORY
LABORATORY MODULE
EVALUATION QUESTION
1. 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.
(b) Determine power delivered to the 2-k resistor using the Thevenin equivalent circuit.
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________
Universiti Malaysia Perlis (UniMAP)
Lab 4 : Thevenin’s Theorem, Norton’s Theorem, Power Transfer