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How Do We Sense, Think, and Move? -- Lab
~ AC DC ~
Important Equipment Warnings for Today's Lesson
- The interface should not be used to measure any voltage greater than ± 10 V. If you see that the signal from the interface is being saturated, then immediately disconnect the circuit (i.e., open the key switch).
- The ammeter should not be used to measure any current greater than ± 5 A. If you see that the needle of the ammeter is pinned at maximum, then immediately disconnect the circuit (i.e., open the key switch).
Task #1 - Measuring AC Voltages Using an Oscilloscope Display
Oscilloscopes are one of the most common instruments used in science, medical technology, and industry and it is important that you gain experience in interpreting information from such a display.
The oscilloscope has the advantage that it can collect data at a very high rate. For example, you can collect up to 250,000 samples/s when using the interface in oscilloscope mode. This makes it ideal for signals that are changing rapidly in time.
Open the file Lab #10 MBL - Scope Display. You should be looking at the following display.
Setting for the scale of the vertical axis (volts/division)
Setting for the scale of the horizontal axis (time/division)
Sampling Rate
When you monitor data, you will notice that the data constantly updates on the screen instead of scrolling off to the right. This makes it easier to analyze certain kinds of signals.
Time is being displayed along the horizontal axis. You can adjust the amount of time
per division with the buttons. The scale currently being used will be displayed above the buttons. Likewise, you can adjust the amount of voltage per division along the vertical direction with the pictured buttons.
Keep in mind that when you change the scale on the oscilloscope display, you are only changing the way the signal is displayed, but you cannot change the actual signal with these settings.
Experiment #1 – Oscilloscope display; Function generator
The function generator can produce output signals of various voltages that change with
time in different ways (square wave , sine wave , and triangular wave .)
- Check that you have a cable with a BNC connector at one end and a double-banana plug at the other connected to the 50 Ω output.
- Plug the double-banana plug into the plastic circuit block.
- Set the amplitude button so that it is closer to MIN than to MAX.
- Set the waveform so that the generator will produce a signal with a sine-wave shape.
- Using the voltage sensor connected to Channel A of the interface, set up a circuit so that you can measure the potential difference across the double-banana plug. Be sure to note which side of the double-banana plug is ground!
- Monitor the data (do not record data at this time!) when you have everything set.
- You will probably need a faster sampling rate (20,000 samples/s or more!) to study the signal from the function generator.
Using this circuit, discuss the answers to the following questions about the scope display with your partners. You do not need to actually write down your answers in your logbook.
(a) How does the displayed signal change if you increase the V/div setting? (b) How does the displayed signal change if you decrease the V/div setting? (c) How does the displayed signal change if you increase the time/div setting? (d) How does the displayed signal change if you decrease the time/div setting?
Using this circuit, discuss the answers to the following questions about the output of the function generator with your partners. You do not need to actually write down your answers in your logbook.
(a) How does the signal change if you increase or decrease the setting of the frequency knob on the generator? (b) How does the signal change if you increase or decrease the value of the depressed scale button? (c) How does the signal change if you increase or decrease the setting of the amplitude knob? (Be sure to keep the amplitude less than 10 V!)
Task #2 - Examining the Behavior of AC circuits with single components
Equipment: Signal generator, Plastic circuit block, Resistor, Banana leads, Ammeter (AC setting), MBL voltage sensors, Digital multimeter
Experiment #2 – R Circuit; AC Signal
Build the following circuit.
V = Signal Generator
R ≈ 220 Ω
R
- +
A
Com.
A
C B
- Be careful to place the ammeter in the circuit with the (-) and (+) in the correct orientation!
- Set the ammeter to the AC scale. The ammeter will give you the "root mean square" value of the current (Irms) passing through the circuit.
- Hook up the Channel A MBL Voltage sensor to measure the voltage across the function generator, VCA = VSignal.
- Hook up the Channel B MBL Voltage sensor to measure the voltage across the resistor, VCB = VR.
- Adjust the Scope display on the software so that you can display a signal for Channels A and B.
- Set the amplitude of the signal from the function generator so that it is near the MIN value (say at 9:00 if the dial were a clock face).
- Set the frequency of the signal from the function generator so that it is small (~ 50 Hz).
Draw a picture of the circuit in your logbook. Include the voltage sensors connected to measure VSignal and VR in your drawing. Clearly label all relevant quantities.
Data Collection Procedure:
- Monitor the data with the Scope display.
- Adjust the axes of the display so you can clearly view the behavior of the two signals.
- Adjust the amplitude of VSignal so that it is about 2.0 V as displayed on the scope. This adjustment should be made using the knob on the frequency generator since you want to change the actual signal.
- Slowly vary the frequency of VSignal over a large range (say 50 – 20,000 Hz).
- Adjust the amplitude knob on the generator as needed to keep the amplitude of VSignal at about 2.0 V.
- That is, you want the amplitude of VSignal to remain constant as you change its frequency.
- In words, describe how the voltage across the resistor (VR) changed as you varied the frequency of VSignal. That is, describe how the frequency of VR changed (or didn't change) and describe how the amplitude of VR changed (or didn't change). If the amplitude did change, when was it largest and when was it smallest?
- In words, describe how the rms current (Irms) passing through the circuit changed (or didn't change) as you varied the frequency of VSignal. If the current did change, when was it largest and when was it smallest?
Comparison to Theory
Chapter 23 of your textbook provides a theoretical discussion of the behavior of AC circuits. Based on this discussion, the authors predict the following behavior for a circuit with a resistor and an AC voltage supply.
Vrms = Irms R
R(f) = R
Frequency (Hz)
- Do your experimental results confirm the relation between Vrms and Irms? Explain. Hint! Pick one frequency where Irms ≠ 0 A, and measure Vrms, Irms, and R. Hint! You can measure Vrms with the digital multimeter set to AC.
- Do your answers to questions 2-4 confirm the frequency dependence of the resistance value pictured in the graph? Explain.
- Based on your results, sketch the rms current of this circuit as a function of frequency. Use the same frequency scale pictured in the above graph.
Comparison to Theory
Based on your textbook, the authors predict the following behavior for a circuit with a capacitor and an AC voltage supply.
Vrms = Irms XC
XC =
2 π fC
= Capacitive Reactance
Frequency (Hz)
- Do your experimental results confirm the relation between Vrms and Irms? Explain. Hint! Pick one frequency where Irms ≠ 0 A, and measure Vrms and Irms and calculate XC. Hint! You can measure Vrms with the digital multimeter set to AC.
- Do your answers to questions 7-9 confirm the frequency dependence of the capacitive reactance pictured in the graph? Explain.
- Based on your results, sketch the rms current of this circuit as a function of frequency. Use the same frequency scale pictured in the above graph.
Experiment #4 – L Circuit; AC Signal
Equipment: Signal generator, Plastic circuit block, Inductor, Banana leads, Ammeter (AC setting), MBL voltage sensors
Build the following circuit.
V = Signal Generator L ≈ 25 mH
A
L
- +
A
+
- Com.
D C
- Hook up the Channel A MBL Voltage sensor to measure the voltage across the function generator, VDA = VSignal.
- Hook up the Channel B MBL Voltage sensor to measure the voltage across the inductor, VDC = VL.
- Set the amplitude of the signal from the function generator so that it is about 2.0 V.
- Set the frequency of the signal from the function generator so that it is small (~ 50 Hz).
Draw a picture of the circuit in your logbook. Include the voltage sensors connected to measure VSignal and VL in your drawing. Clearly label all relevant quantities.
Data Collection Procedure:
- Monitor the data with the Scope display.
- Slowly vary the frequency of VSignal over a large range (say 50 – 20,000 Hz).
- Adjust the amplitude knob on the generator as needed to keep the amplitude of VSignal at about 2.0 V.
- That is, you want the amplitude of VSignal to remain constant as you change its frequency.
- In words, describe how the voltage across the inductor (VL) changed as you varied the frequency of VSignal. That is, describe how the frequency of VL changed (or didn't change) and describe how the amplitude of VL changed (or didn't change). If the amplitude did change, when was it largest and when was it smallest?
- In words, describe how the rms current (Irms) passing through the circuit changed (or didn't change) as you varied the frequency of VSignal. If the current did change, when was it largest and when was it smallest?
Comparison to Theory
Based on your textbook, the authors predict the following behavior for a circuit with an inductor and an AC voltage supply.
Vrms = Irms XL
XL = 2 π fL= Inductive Reactance
Frequency (Hz)
- Do your experimental results confirm the relation between Vrms and Irms? Explain. Hint! Pick one frequency where Irms ≠ 0 A, and measure Vrms and Irms and calculate XL. Hint! You can measure Vrms with the digital multimeter set to AC.
- Do your answers to questions 12-14 confirm the frequency dependence of the inductive reactance pictured in the graph? Explain.
- Based on your results, sketch the rms current of this circuit as a function of frequency. Use the same frequency scale pictured in the above graph.
Comparison to Theory
Based on your textbook, the authors predict the following behavior for a circuit with a resistor, capacitor, and inductor in series with an AC voltage supply.
Vrms = Irms Z
Z = R
2
+ ( XL − XC )
2 = Impedance
where ZMinimum occurs when f = f 0 =
2 π LC
RLC Circuit
Frequency (Hz)
- Use the given formula to predict at what frequency Z will be a minimum for your circuit. Compare your prediction to an experimental value. Explain how you are able to experimentally determine the frequency where Z is a minimum. Print a copy of your graph showing VSignal and VR when Z is a minimum.
- Do your experimental results confirm the relation between Vrms and Irms? Explain. Hint! Pick f = f 0 (with the amplitude of VSignal set to 2.0 V) and measure Vrms and Irms and calculate ZMinimum.
- Do your answers to questions 17-20 confirm the frequency dependence of the impedance pictured in the graph? Explain.
- Based on your results, sketch the rms current of this circuit as a function of frequency. Use the same frequency scale pictured in the above graph.
- If someone asked you, "Does the frequency of an AC signal matter in a circuit?" How would you answer? What examples could you give?
End of Lab Cleanup
- Turn off the multimeter and the function generator.
- Unplug all banana leads.
- Return the circuit components (R, L, and C) to the box provided at your station.
