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Phys 212 Lab: The Oscilloscope and AC Circuits
Name: ____________________________ Date: ______________
Name: ____________________________ Lab Sect.: __________
Name: ____________________________ Lab Instructor: ______________________
Goals:
- To learn to use an oscilloscope as a DC voltmeter.
- To learn to use an oscilloscope to study periodic signals.
- To see how the oscillation amplitude of a series RLC circuit depends upon the driving frequency and exhibits resonance at a particular frequency.
- To see the behavior of an RC filter circuit.
Equipment:
- PASCO Universal Interface & voltage probes
- Phys212 LabKit Battery module
- Oscilloscope w/ probes
- RLC circuit board
- Software: Capstone, Microsoft Excel
Introduction:
The oscilloscope is an extremely useful instrument for measuring electrical signals that vary with time. The conventional oscilloscope is essentially like a TV set: it consists of an electron gun that accelerates a beam of electrons towards a phosphor screen (say, along the z -direction). The beam is deflected in the x - y plane by two sets of plates that provide an electric field. To measure a voltage V that varies in a regular manner with time, we provide a periodic voltage to the x -plates that "sweeps" the electron beam from one side of the phosphor screen to the other — when it reaches the far right side, the beam snaps back to its starting position. Then, to measure the waveform of the signal V , we provide the voltage to the y -plates, so that the electron beam goes up and down, depending on the supplied voltage. When these two motions are combined, the net result is a "trace" on the phosphor screen that shows the voltage of the signal as a function of time, much as we might draw on a sheet of graph paper. We will spent the first portion of today’s lab learning how to use the oscilloscope and how to measure timing and voltage information directly from the screen.
The oscilloscope is a powerful tool, but our primary concern is to use it to help us visualize and understand alternating current (AC) circuits. This will involve some concepts that you are probably still covering concurrently in the lectures and recitations, so we will only cover very basic ideas in this lab. You are already familiar with Ohm's Law: for an ohmic resistor, V = iR. This relationship is valid for the voltage V and current i at any given instant in time, and could tell us the current which flows through a known resistance R when connected to a given voltage supply
V. In direct current (DC) circuits, the current and voltage do not change with time. In an AC circuit, however, we typically apply a periodic signal, the simplest of which is sinusoidal:
V = V 0 sin( ω t ).
Note that ω is the angular frequency (measured in radians per second), and is related to the oscillation frequency f by ω = 2 π f.
If we applied this sinusoidal voltage source to a resistor, then Ohm’s law would tell us that the current through the resistor at any instant of time would be given by
(^0) sin( t ) I 0 sin( t ) R
V
R
V
i = = ω = ω.
Note that every time the voltage V reaches a maximum, the current i reaches a maximum. The same is true for the voltage and current reaching zero or a minimum. We then say that, for a resistor, the voltage and current are "in phase." Note also that Ohm’s law relates the amplitudes V 0 and I 0.
This behavior is not the same for a capacitor or an inductor when connected to a sinusoidal voltage source. This is because the voltage and current in these devices are related to each other through a time derivative. For instance, the voltage across an inductor is proportional to the rate of change of current ( di / dt ) and not simply to i. For inductors and capacitors, the voltage and current are not in phase. You will learn, in fact, that for a single inductor or a single capacitor connected to a sinusoidal source, the current and voltage are 90° out of phase. In other words, when V reaches a maximum or minimum, i is zero and vice-versa. For a capacitor, the current i is 90° ahead of the voltage, and in an inductor, the current is 90° behind the voltage. The amplitudes I 0 and V 0 are related to each other by something that sort of looks like Ohm's Law:
( ) foran inductor
foracapacitor
0 0 0
0 0 0
V I X I L
C
I
V I X
L
C
(Eq. 1)
Note that the quantity that looks like a "resistance" (technically called a "reactance") changes with frequency! From Eq. 1, we can see that a capacitor acts like it has a high reactance at low frequencies and a low reactance at high frequencies, while for an inductor it's the other way around.
Today's lab will focus on a "series RLC " circuit in which we connect a resistor, a capacitor and an inductor in series with a sinusoidal voltage. (We will use the oscilloscope to observe what happens as we vary the frequency of the driving voltage). The circuit is as shown below:
The front panel of this instrument is divided up into five areas:
- To the far left is the display – this shows your voltage vs time AND your current settings on the bottom and side of the graph.
- The next vertical strip contains 6 buttons – these you can use to adjust settings as needed.
- The next are contain controls related to input (Channel 1 and Channel 2) and a knob with a time dial (SEC/div for the x-axis). The rightmost area has the trigger controls for timing the sweep of data recording.
Once the power is on:
- Make sure the green light is on for CH
- Turn the sec/div dial until the time per division is: 2 ms (2 millisecond/cm) – this is written on the bottom of the display next to the “M”.
- Click TRIG MENU button on the right side, check and make sure it says Mode= Auto on the display.
Lab Activity 1: Using the oscilloscope as a DC voltmeter
- Your scope should already have a co-axial cable connected to the "Ch 1" input. The red connecting wire will be connected to the positive end of any voltage you want to measure, while the black connecting wire will be connected to the negative (ground) terminal. In general, it is important to keep to this convention to avoid potentially serious short circuits!
- Note the knob above the CH1 port is the "CH 1 Volts/div" control knob. The Volts/div are written on the bottom right of the screen next to the blue Ch1.
- Connect the red and black ends of the cable to each other to provide a clear input of 0 V.
- Adjust the Ch 1 controls as follows: o Position: adjust this so that the horizontal line is in the center of the display (use the “VERTICAL POSITION knob above the “MATH” button). o Volts/div: set this 1 V/div. This means that every vertical displacement of 1 cm ( one box on the display scale) corresponds to 1 V. (Throughout this lab you should adjust this setting as necessary to obtain more accurate measurements) o Push the “CH 1” button. Check that the “Coupling” is set to DC on the digital display, if not push F1 until it says so.
- Now connect a 1.5-V battery across the scope input, with the black connector to the "negative" terminal and the red connector to the "positive" terminal.
- Note down the vertical deflection of the display line (how many boxes). Try to set the "volts/div" dial to a value that will give you the most accurate reading.
- Repeat the above with the two batteries in series.
Q1. Write down the readings you obtained above.
Single battery
volts/div
vertical deflection [cm]
voltage [V]
Two batteries in series
volts/div
vertical deflection [cm]
voltage [V]
Lab Activity 2: Using the scope to measure the amplitude and frequency of a periodic voltage signal
Now, it's time to learn how the scope can be used to measure a voltage signal that varies with time. We'll be using a signal that is provided by the PASCO Universal interface box.
- First, make sure that there is a pair of wires that are connected to the PASCO Universal interface box at the "output" banana plug outlets (extreme right).
- Connect the scope leads to the output leads from the interface box, making sure you connect the black lead to ground and the red one to the positive output.
- Set the scope "CH 1 VOLTS/DIV" controls to measure 1 volt/div.
- Set the "sec/div" knob to "5 ms."
- Make sure that the PASCO interface is powered on (the power button should be glowing blue light)
- Open PASCO Capstone
- Click on “Signal Generator” on the far left. Click on the drop down menu for “550 Output”, and choose the waveform to be, “Sine”.
- Set the frequency to be 100Hz, and set the amplitude to be 1V.
- Click the “On” button below the “Offset and Limits” dropdown menu.
- Observe the oscilloscope display. You should see a sine wave. Discuss amongst your group how the pattern on the screen is quantitatively related to the frequency of the input signal.
- Try turning the "sec/div" knob to different values and observe how the display changes.
- Try varying the frequency of the Capstone output signal from 30 Hz to 300 Hz. Observe how the oscilloscope display changes and use the "sec/div" knob to keep the display at a convenient scale. Does changing this setting change the frequency of the signal?
Q2. Suppose you want to measure the frequency of a periodic input signal using the scope. Describe how you would go about doing this, i.e. , write down a relationship between the frequency f of the signal, the setting on the "sec/div" scale, and the size of the pattern on the scope’s grid (“size of the pattern” means either the horizontal or vertical properties of the waveform, it is up to you to decide which).
Q2a: Measure the frequency using the oscilloscope and compare it to PASCO.
Lab Activity 3: Using the oscilloscope to analyze a series RLC circuit
Table 1 Measured voltage amplitude across resistor in a series RLC circuit as a function of driving frequency
Q4. Using an Excel spreadsheet, plot the voltage amplitude versus frequency. Include a copy of the graph here.
Q5. At approximately what frequency is the voltage amplitude a maximum? (Again, this is known as the "resonant frequency" of the circuit.)
Resonant frequency (f not ω): _______________________
Q6. We saw in the introduction that the impedance Z is a minimum at this particular "resonant" frequency. Based on the expression for the impedance Z in Eq. 3 and the condition described above, derive a relationship between the resonant angular frequency ω 0, the capacitance C, and the inductance L. Be sure to show how you arrived at your result.
Use this relationship and the value of C = 100 μF to deduce the value of the inductance L :
Q7. Now, we will investigate the effect of the iron bar on the circuit. Remove the iron bar from the inductor, set the frequency to 300 Hz and repeat the process of finding the resonance peak (you do not need to take as many data points without the iron bar, but make sure that you have some on each side of the resonance peak). Include a plot with the data you took with and without the iron bar in your report. How does the iron bar change the inductance?
Q8. Remove the inductor from the circuit to just make an RC circuit, where you are still measuring the voltage across the resistor. Predict the behavior of this circuit (you should be able to be quantitative) as you sweep across frequencies, from high to low values of f.
Q9. Sweep across frequencies, from high to low values of f ., and describe your observations below. How do your observations relate (qualitatively and quantitatively) to your predictions in Q8?
