Lab4 - Capacitors and Capacitive
Reactance (Xc)
OBJECTIVES
After completing this exercise, you should be able to:
• Explain the relationship between voltage and current in a capacitive circuit.
• Explain the relationship between capacitive reactance and frequency.
• Determine capacitive reactance using Ohm’s law.
DISCUSSION
A capacitor acts, in many ways, like the mirror image of an inductor. In the first section of this exercise,
you will verify that capacitor voltage lags capacitor current by 90°, as illustrated in Figure 1. To observe
this phase relationship, you will once again employ a sensing resistor to produce a voltage that is in phase
with the circuit current. This voltage can then be used to verify the phase relationship between capacitor
current and voltage. In the second part of this exercise, you will verify the relationship between capacitive
reactance (Xc) and frequency. As you will see, Xc varies inversely with frequency
Figure 1 The phase relationship between capacitor voltage and current.
PROCEDURE
Part 1: The Phase Relationship Between Capacitor Current and Voltage
1.
Construct the circuit shown in Figure 2 in Proteus ISIS. Note the following:
a. Connecting Channel 1 (Cl) of the oscilloscope to point A allows you to monitor the voltage across the entire
circuit. Since Rs << Xc at the circuit operating frequency, VRS << VC. Therefore, the waveform displayed on
Channel 1 can be assumed to represent Vc.
b. Connecting Channel 2 (C2) of the oscilloscope to point B allows you to measure the voltage across the
sensing resistor. Because the resistor voltage and current are in phase, VRS is in phase with the capacitor
current. As a result, the oscilloscope waveforms represent the phase relationship between Vc (Channel 1)
and Ic (Channel 2).
AC Circuits I – Lab 4
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Vs=10VPP@2KHz
Figure 2
2.
Set the signal generator for a 10 VPP sine wave at a frequency of 2 kHz. Adjust the vertical sensitivity
(volts/div) setting for Channel 2 so that the two waveform displays are approximately equal in size. (They
should appear similar to those shown in Figure 1.)
3.
Draw the two waveforms to scale in Figure 3.
4.
Perform an Analogue analysis. Capturing the loop current I T and the capacitor voltage VC on the same
graph. Include this graph in your report.
Figure 3
Part 2: Capacitive Reactance and Frequency
5.
Construct the circuit shown in Figure 4 in Proteus ISIS . Set the output of the signal generator for an 8 VPP
sinewave at a frequency of 2 kHz. Use Channel 1 of the oscilloscope to display the output of the generator,
and use Channel 2 to display the voltage across R1.
AC Circuits I – Lab 4
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Vs=8VPP@2KHz
Figure 4
6.
Measure the peak-to-peak value of VR1. Record your measurement in Table 1.
Table 1
Frequency
2KHz
5KHz
10KHz
15KHz
25KHz
75KHz
150KHz
7.
VR1
IT
VC
XC = VC/IT
XC = 1/2πfC
Repeat Step 5 for frequencies of 5 kHz, 10 kHz, 15 kHz, 25 kHz, 75 kHz, and 150 kHz. Make certain that the signal
applied to the circuit remains at 8 VPP when you change frequencies. Enter your results in Table 1.
Vs=8VPP@2KHz
Figure 5
8.
Reverse the position of the components as shown in Figure 5 so that Channel 2 displays the voltage across the
capacitor. Repeat Steps 5, 6, and 7, and record the values of VC in Table 1.
AC Circuits I – Lab 4
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9.
Using the values of VR1 and R1, calculate IT for each frequency. Enter your calculations in Table 1.
10. Using the values of IT and VC from Table 1, calculate XC. Enter your calculations in Table 1.
11. Using the frequencies listed in Table 1, complete the right-hand column in that table.
12. Using the values in the right-hand column in Table 1, plot a curve representing the relationship between capacitive
reactance and frequency in Figure 6.
Figure 6
QUESTIONS & PROBLEMS
1.
Refer to the waveforms drawn in Figure 3. Do the waveforms appear to be exactly 900 out of
phase? If not, explain any discrepancies.
2.
Explain how you can tell from the results of Step 3 that current leads voltage, rather than the
other way around.
3.
Refer to Table 1 and curve in Fig 6. Explain what these results tell you about the relationship
between frequency and capacitive reactance.
4.
Refer to Table 1. Did the two methods of calculating capacitive reactance XC agree with each
other? If not explain and discrepancies
5.
Refer to Table 1 Explain why circuit current increased as frequency increased.
AC Circuits I – Lab 4
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