Physics Lab 212P-2



Physics Lab 151/251 Lab 8

The Oscilloscope & AC Circuits

Software List

Science Workshop

Microsoft Excel

Equipment List (all items marked with * are in the student kit, others are supplied at the time of the lab)

RLC circuit board

Oscilloscope + cable

Science Workshop Interface + voltage probes

*Connecting wires with alligator clips

*Two 1.5 V batteries in holder

Lab Activity: The Oscilloscope and AC Circuits

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 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, we provide the measured voltage to the y-plates, so that the electron beam goes up and down, depending on the supplied voltage.

In this lab, you are provided with an oscilloscope. The front panel of this instrument is divided up into six areas:

• To the far left is the cathode ray tube (CRT) display.

• The next vertical strip contains 6 items, including the power button.

• The next two areas contain controls related to the vertical deflection of the electron beam (Channel 1 and Channel 2).

• The last two areas on the right contain controls for the horizontal deflection of the electron beam, including a time base control for determining the rate at which the electron beam will sweep across the display and the trigger controls for timing this sweep.

Before turning the power on, check that the following knobs are in the indicated positions:

1. Auto intensity: turn counterclockwise fully.

2. The three "position" knobs -- Channel 1, channel 2 and horizontal -- pointing up.

3. Vertical mode switches: Channel 1

4. Horizontal mode switch: no dly ("no delay")

5. Sec/Div: 2 ms (2 millisecond/cm)

6. Trigger mode: Auto

Now, push the power switch on. Turn the "Auto Intensity" switch slowly counter clockwise. You should see a line appear on the screen. Keep the intensity at the minimum level required for you to clearly see the line. Prolonged operation at very high intensities can damage the phosphor screen.

If you do not see a line:

• Check whether the scope is plugged in.

• If the scope is plugged in, push the "beam find" button briefly. This should show you that the beam is being deflected in a particularly direction but is off the screen. You can bring the beam back by using the "position" knobs.

Exercise 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 red knob that is part of the "CH 1 Volts/div" control knob. Gently turn this red knob back and forth to get a feel for how it works. Then, turn it clockwise as far as it will go and make sure that it clicks in place. The Channel 1 input is now "calibrated" so that the numbers on the "volts/div" scale are meaningful! Anytime you use a scope, always check that the different scale knobs are in the calibrated position!

• 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:

• Position: adjust this so that the horizontal line is in the center of the display.

• Volts/div: set this to "1" on the 1X side (left side) of the dial. This means that every vertical displacement of 1 cm (major division on the display scale) corresponds to 1 V.

• AC-GND-DC switch for CH 1: set this at DC.

• 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. 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) =

Exercise 2: Using the oscilloscope 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 Science Workshop interface box.

• First, make sure that there is a pair of wires that are connected to the Science Workshop 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 V/div.

• Set the "Sec/div" knob to "5 ms." Make sure the central red knob is in the calibrated position.

• Start "Science Workshop" and click on the "Sample V" icon. A window will open up that allows you to select an output waveform with given amplitude (volts) and frequency (Hertz).

• Set the amplitude to "1 Volt" and the frequency to "100 Hz."

• Select the "sine wave" icon.

• Click the "on" button.

• 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 Science Workshop 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.

Q2. Suppose you want to measure the frequency of an input signal using the scope. Describe how you would go about doing this i.e. write down an equation that relates frequency f, the setting on the "sec/div" scale and the period of the sine wave as observed on the horizontal scale.

Exercise 3: Using the oscilloscope to analyze a series R-L-C circuit

Now for a real circuit measurement! 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 and current at any given instant in time. In DC circuits, these values of course do not change with time. However, suppose you supplied a sinusoidal voltage:

V = V0 sin (ωt)

across the resistor. (Note that ω is angular frequency (radians/sec) and is related to frequency f by ω = 2πf.) Then, Ohm's Law would simple say that:

I = (V0/R) sin (ωt) = I0 sin (ωt).

Note that every time V reaches a maximum, I reaches a maximum. And it's the same for V reaching zero or a minimum. We then say that, for a resistor, V and I are "in phase." Note also that Ohm’s law relates the amplitudes V0 and I0.

This is NOT however true for a capacitor or for an inductor. 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 that they are in fact 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 V, and in an inductor the current is 90( behind the voltage. The amplitudes I0 and V0 are related to each other by something that sort of looks like Ohm's Law:

For a capacitor: V0 = I0 XC = I0/(ωC)

For an inductor: V0 = I0 XL = I0(ωL)

Note that the quantity that looks like a "resistance" (technically called a "reactance") changes with FREQUENCY! So, 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 focuses on a "series RLC" circuit in which we connect a resistor, a capacitor and an inductor in series with a sinusoidal voltage and use the oscilloscope to observe what happens as we vary the frequency of the driving voltage. The circuit is as shown below:

For the series RLC circuit, the amplitude of the current in the circuit is given by:

[pic]

Z is called the "impedance" of the circuit. Now, recall from the earlier page that XL and XC vary with frequency. So, it should be clear that at some particular frequency (called the resonant frequency), Z is a minimum and hence the current in the circuit in the circuit is a maximum. Recalling Ohm's law, if we measure the voltage across R, we are essentially measuring a quantity that is directly related to the current. This is the aim of the last experiment. You have been provided with a circuit board that contains a number of different components connected together. The large white coil is the inductor. To increase its inductance, remove the metal rod that is held on the circuit board and place it vertically in the inductance coil.

• Select the output of the Science Workshop interface box to have amplitude of 1 V and a frequency of 300 Hz.

• Then, connect the output of the interface box across a series combination of the 10 Ω resistor, the inductor and the 100 μF capacitor. Essentially, one lead goes to the free end of the resistor and the other goes to the free end of the capacitor.

• Making sure that you keep the polarities right, connect the input leads of the oscilloscope across the 10 Ω resistor.

• Both the black lead of the oscilloscope and the black lead of the output from the Science Workshop interface are hooked internally to a common “ground”. If these leads are not connected to the same point in your circuit, then the circuit is connected to ground (V = 0) at two different points and you will not be measuring what is intended. If this is the case, rearrange your circuit so as to have the black leads connected together, the output of the interface box across the series combination and the oscilloscope across the resistor.

• Your aim will be to measure the amplitude of the voltage across the resistor as a function of frequency of the output voltage. Vary the frequency down from 300 Hz to 30 Hz in the following steps, measuring the amplitude of the voltage at every frequency: 300 Hz, 250 Hz, 225 Hz, 200 Hz, 175 Hz, 150 Hz, 125 Hz, 100 Hz, 90 Hz, 80 Hz, 70 Hz, 60 Hz, 50 Hz, 45 Hz, 40 Hz, 35 Hz, 30 Hz. You will have to adjust both the "sec/div" horizontal scale as well as the "Volts/div" vertical scale as you go through this measurement.

Q3. Using an Excel spreadsheet, plot the voltage amplitude versus frequency. Include a printout of the graph with your lab report.

Q4. Approximately at what frequency is the voltage amplitude a maximum? (This is known as the "resonant frequency" of the circuit.)

Resonant frequency = _______________________

Q5. We mentioned earlier that the impedance Z is a minimum at a particular "resonant" frequency. Use the expression for Z to show that the resonant frequency is related to the capacitor and the inductor in the circuit by:

ωR = (LC)-1/2

Use this relationship and the value of C = 100 μF to deduce the value of the inductance L.

-----------------------

V0 sin(ωt)

L

C

R

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