The Oscilloscope and AC Circuits - Laboratory Experiment | PHYS 212P, Lab Reports of Physics

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Physics Lab 212P-10 The Oscilloscope & AC Circuits NAME: ____________________________________ LAB PARTNERS: ____________________________________ ____________________________________ LAB SECTION: __________________________ LAB INSTRUCTOR: __________________________ DATE: __________________________ EMAIL ADDRESS: __________________________ Physics Lab 212P-10 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 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 (t) across the resistor. (Note that  is angular frequency (radians/sec) and is related to frequency f by  = 2f.) Then, Ohm's Law would simple say that: I = (V0/R) sin (t) = I0 sin (t). 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/(C) For an inductor: V0 = I0 XL = I0(L) 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: 22 0 )( , CL XXRZ Z V I   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 resistor, the inductor and the 100 F 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  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. R C L V0 sin(t)