Download Experiment 4

Experiment 4
Thevenin’s Theorem and Power Transfer
John Nosek
ENEE 206
Section 101
Lab Report 4
3/9/04
● Objective
To study Thevenin’s Theorems and use different ways to find Thevenin resistance and
Thevenin Equivalent circuits. Also to study power transfer in circuits.
● Equipment
- DC Power Supply
- Digital Multimeter
- Breadboard
- 20 kΩ Potentiometer
- Following Resistors:
500 Ω
1 kΩ
1.5 kΩ
3 kΩ
2 x 5 kΩ
6 kΩ
7.5 kΩ
2 x 10 kΩ
33 kΩ
62 kΩ
100 kΩ
● Schematics
Figure 1
R2
R5
V12
a
R1 = 1 kΩ
R2 = 5 kΩ
R3 = 5 kΩ
R4 = 10 kΩ
R5 = 7.5 kΩ
R4
R1
R3
V12 = 12 V DC
V6 = 6 V DC
V6
b
● Procedure
Part A involved constructing the circuit in Figure 1 and taking certain
measurements on it to develop the Thevenin Resistance and Equivalent. First, the actual
values of the resistors in the circuit were measured and recorded. The circuit was then
constructed and the open circuit voltage and short circuit current was measure so the
Thevenin Resistance could be found. Since most circuits will not permit shorting of the
output terminals, we used another method to find the Thevenin Resistance. The
potentiometer was connected as a load between terminals a and b and adjusted till the
voltage across it was half of the open circuit voltage. The resistance of the potentiometer
was then taken since it was then equal to the Thevenin Resistance. Using a known
resistor, it was then connected between terminals a and b and the voltage drop across it
was measured so the Thevenin Resistance could be calculated a third way. With the
same resistor still in the circuit, the current through the resistor was measured so another
calculation of the Thevenin Resistance could be made. The voltage sources were then
zeroed out and the resistance at the terminals was measured for a final measurement of
the Thevenin Resistance. Finally, the results were compared and a schematic for the
Thevenin Equivalent Circuit was drawn.
Part B involved measuring the power transfer in the circuit in Figure 1. The
voltage at terminals a and b was measured along with the actual values of the remaining
resistors. All the load resistors were then placed across terminals a and b and the voltage
across them was measured so the power dissipated could be calculated. By plotting the
power dissipated versus the load resistance, the Thevenin Resistance was found again.
This value was compared to the values obtained in Part A.
● Results
Part A
1)
Resistor
R1
R2
R3
R4
R5
3)
Marked Value
1 kΩ
5 kΩ
5 kΩ
10 kΩ
7.5 kΩ
Vopen  5.990 V
I short  0.51 mA
Measured Value
0.995 kΩ
5.057 kΩ
5.050 kΩ
10.15 kΩ
7.360 kΩ
RTH 
Vopen
RTH 
5.990
 11.745 k
0.00051
4)
5)
6)
I short
RTH  R p  12.06 k
R  10.01 k
Vab  2.725 V
Vopen  5.990 V
Vopen
RTH  R

Vab
R
5.990
2.725

 2.72  10  4
RTH  10010 10010
RTH 
7)
5.990
 10010  11.99 k
2.72  10  4
Vopen  5.990 V
R  10.01 k
I R  0.28 mA
RTH 
Vopen
IR
R
5.990
 10010  11.38 k
.00028
RTH measured with sources zeroed out  12.02 k
8)
After comparing the results, it seems that all calculations point to a value
for the Thevenin Resistance being around 12 kΩ. This value corresponds
to the Thevenin Voltage Source of about 6 V and to all calculations
performed.
Thevenin Equivalent Circuit
12 kΩ
a
6 V DC
b
Part B
1)
Vopen  5.991 V
2)
Resistor Values
Marked Value
500 Ω
1.5 kΩ
3 kΩ
6 kΩ
10 kΩ
20 kΩ
30 kΩ
62 kΩ
100 kΩ
Measured Value
507.5 Ω
1.474 kΩ
2.970 kΩ
6.076 kΩ
10.01 kΩ
19.82 kΩ
32.71 kΩ
61.31 kΩ
98.2 kΩ
3, 4, 5)
Resistor
500 Ω
1.5 kΩ
3 kΩ
6 kΩ
10 kΩ
20 kΩ
33 kΩ
62 kΩ
100 kΩ
Voltage Load VL
0.243 V
0.654 V
1.186 V
2.011 V
2.723 V
3.729 V
4.381 V
5.009 V
5.337 V
Power Dissipated (V2/R)
.116 mW
.290 mW
.474 mW
.665 mW
.741 mW
.702 mW
.587 mW
.409 mW
.290 mW
6)
Power Dissipation In Resistors
0.8
0.7
Power (mW)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20000
40000
60000
Resistance (Ω)
80000
100000
7)
Based on the fact that the maximum power transferred is at the load resistance
equal in value to the Thevenin Resistance:
RTH  11 k
8)
This answer and the graph closely represents the values obtain in Part A which
proves the relationship between resistance and power dissipation.
● Conclusion
This lab experiment showed many methods used to find the open circuit voltage,
close circuit current, and Thevenin Resistance needed in order to develop a Thevenin
Equivalent Circuit for a given circuit. Most importantly, it showed the many calculations
that can be done to obtain the Thevenin Resistance and what measurements are needed to
be known in order to perform them. It clearly showed the many relationships involved in
Thevenin Circuits. Also, the final part of the lab showed the relationship that exists
between Thevenin Resistance and the maximum power dissipation in a circuit.