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Name: Lab Partners:
Date:
Pre-Lab Preparation:
Alternating Currents and Voltages
(due at the beginning of lab)
Question 1 What is the meaning of DC? Of AC? Give examples of each in terms of an electrical signal.
Question 2 If the unit for time is the second:
(a) what is the unit for frequency of a time dependent signal?
(b) what is the unit for period of a time dependent signal?
Question 3 Below, draw a sinusoidal signal with one-half the frequency of the signal shown. Draw it on top of the signal shown, using if possible a colored pen or pencil.
Question 4 Below, draw a sinusoidal signal that lags the signal shown by 90 ◦. Draw it on top of the signal shown, using if possible a colored pen or pencil.
PHYS-204: Physics II Laboratory i
Question 5 What does a signal generator provide? How is it different than a battery?
PHYS-204: Physics II Laboratory ii
Voltage Time
Example of Time-varying Signal
There is a special type of time-varying signal. These signals can be used to drive current in one direction in a circuit, then in the other direction, then back in the original direction, and so on. These signals form a pattern that repeats over time, and they are referred to as AC, or alternating current signals.
Voltage Time
Examples of AC Signals
Voltage Time
In the top diagram, the AC signal is a sinusoid that varies smoothly over time. In the bottom diagram, the AC signal changes abruptly from a negative value to a positive value. In Investigation 1, you will create an AC signal using a battery. You will then learn about the signal generator–a device that produces a different types of regular, time-varying AC signals. In Investigation 2, you will learn whether a time-varying signal affects a circuit that contains a resistor. In Investigation 3, you will learn how inductors and capacitors affect both current and voltage in various parts of an AC circuit.
Investigation 1:
Introduction to AC Signals
The purpose of this investigation is for you to learn to use a battery and a signal generator to create time-varying signals. You will use a simple circuit consisting of a battery and a resistor, and will use probes to measure current and voltage in this circuit. You will need the following materials:
- computer with Lab Pro interface
- Logger Pro software
- current probe and voltage probe
- 1.5 V battery
- 100 Ω resistor
- connecting wires
- Pasco signal generator (low output impedance)
In Activity 1-1, you will generate a time-varying signal from a battery’s DC voltage.
Activity 1.1: Introduction to Time-Varying Signals
Fig. 1 shows a circuit consisting of a battery and a resistor, with current and voltage probes.
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R
CP
VP
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Figure 1: Circuit for generating a time-varying signal
In Fig. 2 (a), the circuit diagram in Fig. 1 is redrawn for the case in which the wire labeled A is connected to the positive terminal of the battery, and the wire labeled B is connected to the negative terminal. (Let’s call this Position 1.). The arrow labeled I represents the direction of current through the circuit (the flow of positive charge).
Question 1.1 In the space for Fig. 2(b), sketch the circuit diagram for Position 2, in which you reverse the polarity by disconnecting wire A from the positive terminal and then connecting it to the negative terminal of the battery, and disconnecting wire B from the negative terminal and then connecting it to the positive terminal. Indicate the direction of current on your diagram with an arrow labeled I.
Step 1: Open experiment file L8A1-1 (Time Varying Signal) to open axes similar to those above.
Step 2: Zero the probes with them disconnected from the circuit.
Step 3: Connect the circuit in Fig. 1. Do not connect the battery yet.
Step 4: Begin graphing. Touch your connecting wires to the terminals of the battery alter- nately in position 1 and in position 2, switching back and forth every 2 seconds. (Note: it is much easier to simply hold the ends of the wires against the battery terminals, rather than connect them.)
Step 5: Sketch your graphs of current and voltage vs. time using solid lines on the axes above.
Question 1.3 Do your measured graphs agree with your predicted ones? If not, how do they differ and why?
Question 1.4 What is the peak value of V? (Note: ”peak value” is the same as ”amplitude”.)
Question 1.5 What is the frequency (approximately) of the signal you generated? (Note: fre- quency is the number of cycles per second.) Explain how you determined the frequency. Note: A frequency does not have to be a whole number (i.e., it can be a decimal fraction!)
Activity 1.2: Introduction to the Signal Generator
In the previous activity, you generated a time-varying signal by reversing the polarity of a circuit by hand. As you might imagine, it is difficult to generate a continuous AC signal at a constant frequency with this method. Instruments exist that can create time-varying signals with very regular behavior over time. Not surprisingly, such an instrument is called a Signal Generator.
Step 1: Open experiment file L8A1-2 (Signal Generator). This will set up the voltage probe and software to graph voltage vs. time in Repeat Mode on axes like those that follow.
Step 2: Zero the voltage probe when you have disconnected from the signal generator.
Step 3: Adjust the signal generator to a frequency of 100 Hz (100 cycles/second), and set the amplitude control about half of maximum. Ask your instructor to check the settings in the generator if you have any questions about them.
Step 4: Connect the voltage probe across the signal generator.
Step 5: Begin graphing and measuring the voltage output from the signal generator. Watch the graph for several seconds, and then stop graphing so that your measurements are captured.
Time (s)
Voltage (V)
− (^60) .02 .04 .06 .08.
− 4
− 2
0
2
4
6
Step 6: Sketch your graph on the axes above.
Question 1.6 Compare the signal generated by the signal generator to the one you pro- duced by hand in Activity 1.1. How are they similar, and how do they differ?
Question 1.7 The period T is the time from one peak of a signal to the next. Use the analysis feature to find T (Hint: determine the time period for several peaks and divide by the number of peaks.) Show your calculation.
Question 1.8 The period of a signal is the inverse of the frequency (T = 1/f ). How does your measurement of period compare with the frequency setting on the signal generator? Show your calculation.
Step 7: Begin graphing again with the signal generator set at 100 Hz. While the voltage probe is continuously measuring, reduce the signal frequency of the signal generator to around 50 Hz, and then increase it to 150 Hz.
Vsignal(t) ∼
AC input
R
CP
VP
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Figure 3: Resistor circuit with AC input signal
Prediction 2.1 On the axes below, sketch, with dotted lines, your quantitative prediction for the input signal, Vsignal, vs. t, and the current through the resistor, I vs. t. (Hint: consider Ohm’s Law). Assume a maximum potential of +5.0 volts and a minimum of -5.0 volts.
Time (s)
Current (A)
−. (^060) .02 .04 .06 .08.
−. 04
−. 02
. 00 . 02 . 04 . 06
Time (s)
Voltage (V)
0 .02 .04 .06 .08. − 6
− 4
− 2
0
2
4
6
Test your predictions:
Step 1: Open experiment file L8A2-1 (Resistor with AC).
Step 2: Zero the probes with them disconnected from the circuit.
Step 3: Connect the circuit in Fig. 3.
Step 4: Set the signal generator to a frequency of 100 Hz.
Step 5: Begin graphing. Set the amplitude on the signal generator so that the voltage mea- sured by the voltage probe across the resistor has an amplitude of 5 volts (+5V maximum and -5V minimum). When you have a good graph of the signal, stop graphing.
Step 6: Sketch your graphs on the axes above. Pay attention to how the peaks in the current graph line up with the peaks in the voltage graph. Do they occur at the same time, or are the peaks in one graph ahead of the other? Be sure your sketch represents both graphs.
Step 7: On the graph of voltage vs. time, identify and label a time when the current (yes, the current) through the resistor is maximum.
Step 8: On your graph of current vs. time, identify and label a time when the voltage (yes. the voltage) across the resistor is maximum.
Question 2.2 Does a voltage maximum occur at the same time as a current maximum, or does one maximum (current or voltage) occur before the other? Explain.
Step 9: Use your graph to complete Column I in Table 1. To get information from the graph, you can use the analysis feature. Select several cycles by highlighting them, and then you can use the statistics feature to find the maximum values for the voltage and current.
f = 100 Hz f = 200 Hz f = 300 Hz At maximum voltage, At maximum voltage, At maximum voltage, the current is (circle one): the current is (circle one): the current is (circle one):
Maximum Maximum Maximum Minimum Minimum Minimum Zero and increasing Zero and increasing Zero and increasing Zero and decreasing Zero and decreasing Zero and decreasing Nonzero and increasing Nonzero and increasing Nonzero and increasing Nonzero and decreasing Nonzero and decreasing Nonzero and decreasing Other Other Other
Max. voltage (Vmax) Max. voltage (Vmax) Max. voltage (Vmax) Max. current (Imax) Max. current (Imax) Max. current (Imax) R = Vmax/Imax = R = Vmax/Imax = R = Vmax/Imax =
Table 1: AC Signals and Resistors
Step 10: Set the frequency of the signal generator to 200 Hz. Be sure that the amplitude is still 5V. Graph I and V as before. Use the analysis feature to complete Column II in Table 1.
Step 11: Set the frequency of the signal generator to 300 Hz. Check that the amplitude is still 5V. Graph I and V as before, and complete Column III in Table 1.
Activity 3.1: AC Signals and Capacitors
Does the impedance of a capacitor change when the frequency of the applied signal changes? In this activity, you will investigate this question by measuring the behavior of a capacitor when signals of various frequencies are applied to it. Specifically, you will look at the amplitude and the phase of the current through and voltage across it. Comment: When the peak current through and voltage across a circuit element always occur at the same instant the current and voltage are said to be in phase. In Activity 2-1, you observed the AC current-voltage characteristics of a resistor. What you should have determined is that the current and voltage are in phase for a resistor. When the peak current occurs at a different instant than the peak voltage, there is a phase difference. The current and voltage are then said to be out of phase. The phase difference can be expressed in degrees, radians, or fractions of a period. Consider the circuit shown in Fig. 4.
Vsignal(t) ∼
AC input
C
CP
VP
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Figure 4: Capacitor circuit with AC input. For best results use C ' 7 μF.
Prediction 3.1 Suppose that you replaced the signal generator with a battery and a switch. The capacitor is initially uncharged, and therefore the voltage across the capacitor is zero. If you close the switch, which quantity reaches its maximum value first: current in the circuit or voltage across the capacitor? (As charge builds up on the capacitor, and the voltage across the capacitor increases, what happens to the current in the circuit?) Explain.
Prediction 3.2 At the instant the capacitor reaches its maximum charge (and maximum volt- age) for this circuit, what do you predict the magnitude of the current will be–maximum, mini- mum or zero? Why? At this instant, what must be the value of the voltage across the capacitor –maximum, minimum or zero?
Prediction 3.3 The actual AC voltage applied to the circuit in Fig. 4 by the signal generator is shown on the axes that follow. Use your answers from the above questions to sketch with dotted lines your prediction for the current as a function of time.
Time (s)
Current (A)
0 .01 .02 .03 .04. −. 06
−. 04
−. 02
. 00 . 02 . 04 . 06
Time (s)
Voltage (V)
− (^60) .01 .02 .03 .04.
− 4
− 2
0
2
4
6
Test your predictions.
Step 1: Open the experiment file L8A3-1 (Capacitor).
Step 2: Zero the probes while disconnected from the circuit.
Step 3: Connect the circuit in Fig. 4.
Step 4: Set the signal generator to a frequency of 100 Hz.
Step 5: Begin graphing. Set the amplitude to 5 volts (+5V maximum and -5V minimum). When you have a good graph of the signal, stop graphing.
Step 6: Sketch your graphs on the axes above. Pay attention to how the peaks in the current graph line up with the peaks in the voltage graph. Do they occur at the same time, or are the peaks in one graph ahead of the other? Be sure your sketch represents how the two graphs are correlated.
Step 7: On the graph of voltage vs. time, identify and label a time when the current (yes, the current) through the capacitor is maximum.
Step 8: On your graph of current vs. time, identify and label a time when the voltage (yes. the voltage) across the capacitor is maximum.
Step 9: Clearly mark one period of the AC signals on your graphs.
Question 3.1 Does your measured current graph agree with your predicted one? If not, how do they differ?
Then repeat with the signal generator set at 300 Hz, and complete column 3.
Question 3.3 What can you say about the magnitude of the reactance of the capacitor at 100Hz compared to the reactance of the capacitor at 200Hz? What happens to the reactance as the frequency was increased to 300 Hz? Explain based on your observations.
Question 3.4 What can you say about the phase difference between current and voltage for a capacitor at 100 Hz compared to the phase difference at 200 Hz? What happens to the phase difference as the frequency increases to 300 Hz. Explain based on your observations.
Activity 3.2: Inductors and AC Signals
Consider the circuit shown in Fig. 5.
Vsignal(t) ∼
AC input
L
CP
VP
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Figure 5: Inductor circuit with AC input.
Prediction 3.4 Suppose that you replaced the signal generator with a battery and a switch. The inductor initially has no current through it. If you close the switch, which quantity reaches its maximum value first: current in the circuit or voltage across the inductor? (Hint: the inductor acts like inertia in the circuit-it prevents rapid changes in the current by setting up a voltage that opposes the change.) As the current builds up in the circuit, what happens to the voltage which is induced across the inductor? Explain.
Prediction 3.5 At the instant the current reaches its maximum value for this circuit, what do you predict the magnitude of the induced voltage will be–maximum, minimum or zero? Why?
Prediction 3.6 The actual AC voltage applied to the circuit in Fig. 5 by the signal generator is shown on the axes that follow. Use your answers from the above questions to sketch with dotted lines your prediction for the current as a function of time.
Time (s)
Current (A)
0 .01 .02 .03 .04. −. 06
−. 04
−. 02
. 00 . 02 . 04 . 06
Time (s)
Voltage (V)
0 .01 .02 .03 .04. − 6
− 4
− 2
0
2
4
6
Test your predictions.
Step 1: Open the experiment file called L8A3-3 (Inductor).
Step 2: Zero the probes while disconnected from the circuit.
Step 3: Connect the circuit in Fig. 5.
Step 4: Set the signal generator to a frequency of 100Hz.
Step 5: Begin graphing. Set the signal generator amplitude to 5 volts (+5V maximum and -5V minimum). When you have a good graph of the signal, stop graphing.
Step 6: Sketch your graphs on the axes above. Pay attention to where the peaks in the current graph occur in comparison with the peaks in the voltage graph. Do they occur at the same time, or are the peaks in one graph ahead of the other? Be sure your sketch represents how the two graphs are correlated.
Step 7: On the graph of voltage vs. time, identify and label a time when the current (yes, the current) through the capacitor is maximum.
Step 8: On your graph of current vs. time, identify and label a time when the voltage (yes, the voltage e) across the capacitor is maximum.
Step 9: Clearly mark one period of the AC signals on your graphs.
Then increase the frequency to 300 Hz, and collect the data needed for the last column in Table 3.
Question 3.7 What can you say about the magnitude of the reactance of the inductor at 100Hz compared to the reactance of the inductor at 200Hz? What happens to the reactance as the frequency was increased to 300 Hz? Explain based on your observations.
Question 3.8 What can you say about the phase difference between current and voltage for an inductor at 100 Hz compared to the phase difference at 200 Hz? What happens to the phase difference as the frequency increases to 300 Hz? Explain based on your observations.
This laboratory exercise has been adapted from the references below.
References
[1] David R. Sokoloff, Priscilla W. Laws, Ronald K. Thornton, and et.al. Real Time Physics, Active Learning Laboratories, Module 3: Electric Circuits. John Wiley & Sons, Inc., New York, NY, 1st edition, 2004.
[2] Priscilla W. Laws. Workshop Physics Activity Guide, Module 4: Electricity and Magnetism. John Wiley & Sons, Inc., New York, NY, 1st edition, 2004.
[3] Lilian C. McDermott, et.al. Physics by Inquiry, Volumes I & II. John Wiley & Sons, Inc., New York, NY, 1st edition, 1996.
