Sample Lab Report - Milwaukee Area Technical College

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
BACKGROUND INFORMATION
Use KVL to determine the fundamental properties of AC series circuits. Voltage and
currents can be calculated for all components in the AC series circuit.
THEORETICAL SOLUTION
R 1
1 k
V S1
1 V P-P
R 2
2.2 k
R 3
820
Circuit One
Figure 15-1: Test circuit 1
R T R 1 R 2 R 3
R 1
VR 1 V S
R T
VR 1 0.249V
R 2
VR 2 V S
VR
R 2 0.547V
T
R 3
VR 3 V S
R T
VR 3 0.204V
V S VR 1 VR 2 VR 3
0V
1

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
R 1
1 k
V S1
2 V P-P
R 2
2.2 k
C 1
0.01 F
Figure 15-2: Test circuit 2
jXC i
Circuit Two Z R i 1 R 2
R 1
R XC 2
i
VR1 V i S VR2 V
Z i S
VC1 V
Z i S j
Z i
i
i
5.045 10 4 0.013i
0.012 0.06i
VR1 i
0.043 0.108i
0.083 0.138i
0.998 0.04i
0.961 0.193i
VC1 i 0.861 0.346i
0.733 0.442i
V
V
VR1 VR2 i i
1.11 10 3 0.028i
0.027 0.133i
VR2 i
0.096 0.238i
0.183 0.304i
VC1 i
V S
0
0
0
0
V
V
2

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
VR1 i
0.013
0.062
0.117
0.161
V
180
arg VR1 i π
87.697
78.632
68.094
58.902
VR2 i
0.028
0.136
0.256
0.355
V
180
arg VR2 i π
87.697
78.632
68.094
58.902
VC1 i
0.999
0.98
V
180
arg VC1 i π
-2.303
-11.368
0.928
-21.906
0.856
-31.098
Simulations:
U1
+ -
0.249 V
AC 10M
U2
+ -
0.547 V
AC 10M
3
R1
1 2
1k
R2
2.2k
V1
1 V
60 Hz
0Deg
R3
820
0
+
-
0.204 V
U3
AC 10M
Figure 15.3: Simulation of test circuit one.
3

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
1
R1
1k
2
R2
2.2k
3
V1
1 V
60 Hz
0Deg
0
C1
0.01uF
Figure 15.4: Simulation of test circuit two.
Procedure
Figure 15.2 Simulation Results
V R1 V R2 V C1
Freq Mag Phase Mag Phase Mag Phase
1000 0.0616 78.63 0.1355 78.63 0.9804 ‐11.37
2000 0.1166 68.09 0.2565 68.09 0.9278 ‐21.91
3000 0.1614 58.90 0.3551 58.90 0.8563 ‐31.10
RESULTS
Connect the circuit shown in Figure 15.1. Measure and record the voltage across R 1 , R 2 ,
and R 3 . Next connect the circuit shown in Figure 15.2. Measure and record the voltage
across all components.
Data
Figure 15-1
Simulation Results
Frequency V R3 V R2 V R1 Node 2 KVL Phase
200 0.20398 0.547264 0.248756 0.751244 0 0
1000 0.20398 0.547264 0.248756 0.751244 0 0
2000 0.20398 0.547264 0.248756 0.751244 0 0
3000 0.20398 0.547264 0.248756 0.751244 0 0
Figure 15-2
Theoretical Results
Frequency V R3 V R2 VR1
4

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
200 0.204 0.547 0.249
Figure 15-2
Measured Results
Frequency V C Phase V R2 Phase V R1 Phase
2000 0.921934 -23.219 0.264667 66.325 0.118386 66.923
3000 0.832818 -33.938 0.376791 55.595 0.169122 56.027
Figure 15-2
Theoretical Results
Frequency V C Phase V R2 Phase V R1 Phase
2000 0.928 -21.906 0.256 68.094 0.117 68.094
3000 0.856 -31.098 0.355 58.902 0.161 58.902
Figure 15.2 Simulation Results
V R1 V R2 V C1
Freq Mag Phase Mag Phase Mag Phase
1000 0.0616 78.63 0.1355 78.63 0.9804 ‐11.37
2000 0.1166 68.09 0.2565 68.09 0.9278 ‐21.91
3000 0.1614 58.90 0.3551 58.90 0.8563 ‐31.10
ANALYSIS OF RESULTS
Since test circuit one was purely resistive, a DMM or oscilloscope could be used to
measure the voltage drops across the resistors. KVL could be verified for each
frequency.
5

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
5.045 10 4 0.013i
0.012 0.06i
VR1 i
0.043 0.108i
0.083 0.138i
0.998 0.04i
0.961 0.193i
VC1 i 0.861 0.346i
0.733 0.442i
V
V
VR1 VR2 i i
1.11 10 3 0.028i
0.027 0.133i
VR2 i
0.096 0.238i
0.183 0.304i
VC1 i
V S
0
0
0
0
V
V
Since in test circuit two R 3 was replace with a capacitor. A capacitor is a reactive
component. The impedance of the capacitor changes inversely with the frequency.
Therefore a DMM can not be used to verify KVL. The DMM only provides magnitude
information. An oscilloscope was needed to obtain the phasor voltage associated with the
reactive circuit.
There were no significant errors in measurement during this experiment.
EXECUTIVE SUMMARY
This experiment verified KVL for a series AC circuit. A purely resistive circuit and a
reactive circuit were examined. It was found that a DMM or oscilloscope could be
utilized to verify KVL for a purely resistive circuit. A DMM could not be utilized for
verify KVL in a reactive circuit. A DMM only provides magnitude information. A
reactive circuit is complex and both magnitude and phase data are required. An
oscilloscope is needed to obtain the required data for the reactive circuit. The addition of
the capacitor is reflected in the phase angle information obtain. Recall that the current in
6

Experiment 15 Richard Lokken 8/21/2009
Milwaukee Area Technical College ELCTEC-112
a capacitor leads the voltage by 90 o . This is because the plates require time to charge to
the full voltage. Once fully charge the capacitor resembles an open circuit. This stored
voltage is then available for use in the circuit.
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