Lab 3 - Capacitors. Stony Brook Physics Laboratory Manuals. Equipment

Transcription

1 3/20/2017 Lab 3 Capacitors [Stony Brook Physics Laboratory Manuals] Stony Brook Physics Laboratory Manuals Lab 3 - Capacitors In this experiment we will determine the capacitance of an unknown capacitor by observing the change in potential difference between its plates when, after being initially charged, it is connected in parallel with a known capacitor. We will also study the behavior of capacitors connected in series. Equipment Oscilloscope (you should review what you learned about the oscilloscope in Lab 2) Unknown capacitor C1 Capacitor box to provide C2 in 1μF (one microfarad) steps between 0-10μF Double-pole double-throw (DPDT) switch test leads with banana plugs at each end alligator clips (their tube ends slide over the banana plugs their teeth grip a terminal) Dry cell with potential difference (voltage) V0 Figure 1 shows the same closeup picture of an oscilloscope you had for Lab 2. Once again, it may be the same model as the one you will use or it may be a slightly different model that looks nearly the same. It doesn't make any difference which oscilloscope you actually use during the lab. What's important is that you use it correctly. Note that the two (vertical) inputs are labeled CH1<color white/gray>x</color>. and CH2<color white/gray>y</color> in Fig. 1. Just pay attention to the label CH1, which is the channel you will be using in this experiment. Note in Fig. 1 that the 3-position lever switch to the left of the VOLTS/DIV know for CH1 is set to AC. This means AC coupling, which is what you do NOT want for this experiment. This places a capacitor (inside the oscilloscope) in series with the signal entering CH1, and this capacitor blocks the DC value, which is what you want to measure. Therefore, move the lever switch for CH1 to DC, the lowest position. Make sure the VERT MODE lever switch is on CH1 (the top-most position), just as it's shown in Fig. 1. Also make sure that the red VAR knob for CH1 (do the same for CH2, also) is full clockwise, the calibrated position as you learned in Lab 2. While you're at it, make sure the VAR SWEEP knob is also full clockwise, and make sure that the white <color white/gray>x-y</color> switch is out so that the oscilloscope is not in the XY mode of operation. (You used that mode to see the Lissajous figures in Lab 2.) Rule of thumb for using oscilloscopes: Always use DC coupling unless you have a specific reason not to! 1/6

2 3/20/2017 Lab 3 Capacitors [Stony Brook Physics Laboratory Manuals] Figure 2 shows two capacitor boxes. We don't have enough of one type to provide all 24 work stations in the two lab rooms with the same type. However, they're functionally equivalent so it doesn't make any difference which one you use. Each one has two banana sockets for making connections to its two plates and one knob on a rotary switch that selects the value of C2. In Fig. 2, each knob is set for 1μF (one microfarad). Figure 3 shows the unknown capacitor C1. You know it's a capacitor, but you don't know its value. That's why you're going to measure it! There are two terminals at the top with each one connected to one of the plates inside. (You can see that each terminal has two metal prongs sticking out which prong you connect to (with an alligator clip at the end of a test lead ) at a given terminal is not important.) Method In Part I, a capacitor C1 is charged to potential V0 by using a double-pole-double-throw (DPDT) switch (learn about electrical switches here) to connect one of its two ends (terminals) to one terminal of a dry cell battery and its other end (terminal) to the other terminal of the dry cell battery. This is frequently called connecting the capacitor across the dry cell. Is the resulting circuit consisting of the battery and the capacitor C1 a series circuit? Or is it a parallel circuit? 2/6

3 The dry cell is then disconnected, and an initially uncharged capacitor C 2 is connected (by moving the handle on the DPDT switch to the other position) to C 1 as follows: one of the two ends (terminals) of one capacitor is connected to one of the two ends (terminals) of the other capacitor, and the two other ends (terminals) are connected to each other. (Note that this makes a circuit with the shape (topology) of a ring. Is it a series circuit or a parallel circuit?) Charge will flow from C 1 to C 2 until the potential differences across the two capacitors equalize. (Why does this happen?) The voltage across the two connected capacitors (which you can think of as one equivalent capacitor C eq is given by: V = V 0 C 1 /( C 1 + C 2 ) (1) Derive Eq. (1) in your lab notebook. Rearranging Eq. (1) gives V 0 / V = C 2 / C (2) C 2 is an adjustable capacitor. As C 2 is changed, the final voltage V will vary according to Eqs. (1) and (2). In Part II, a similar procedure using the double-pole-double-throw switch connects the two capacitors together. How is the connection different this time? Does this way of connecting them make a series circuit or a parallel circuit? Note that in all figures below, there is more than just capacitors and just capacitors and a battery and a DPDT switch in the electrical circuits. There is also a measuring instrument the oscilloscope! that must become part of the circuit for you to be able to measure the voltage differences that show you what's going on. Note further that some of the figures do NOT show the DPDT switch. Instead one figure shows you the circuit that's created for one position of the DPDT switch handle; a second figure shows you the circuit that's created for the other position of the DPDT switch handle. Procedure 1. Capacitors in Parallel C 1 is a fixed capacitor whose capacitance is to be measured. C 2 is a capacitance box with capacitance variable from 0 to 10 microfarads ( μf) in 1 μf steps. With the DPDT switch in position (1), C 2 is discharged and out of the circuit and C 1 is charged to the voltage of the battery V 0 and in the circuit. This voltage can be read on the oscilloscope, in the same way as the battery 3/6

4 voltage was measured in Lab 2. Note: you need to insert a wire in the place of the switch (2) position, depicted by the red oval in the picture above. With the DPDT switch in position (1), the battery is connected and charges C 1, see above. With the DPDT switch in position (2), the battery is disconnected, C 1 and C 2 are connected in parallel, and the voltage across the parallel combination can be read on the oscilloscope. 1. Connect the circuit as shown. 2. Move the DPDT switch to position (1) to discharge C 2 and charge C 1. Then move the DPDT switch to position (2) and record the voltage V immediately appearing on the oscilloscope. This voltage will decay to zero as time passes; its value immediately after the DPDT switch is thrown is what you must record. Repeat the measurements several times so that you can estimate the uncertainty in this voltage. Why does the voltage decay? 3. Repeat the above procedure using at least 5 other values of C 2. For each value of C 2 you should have a value of V and an estimate of the uncertainty in its value. 4. Make a plot of V 0 /V vs. C 2. Determine C 1, the unknown capacitance, from this plot by referring to Eq. (2). 2. Capacitors in Series 4/6

5 In this arrangement, DPDT switch in position 1, two capacitors connected in series are initially uncharged. This makes the circuit like that below. When the DPDT switch is thrown to position (2), the series combination is connected to a potential difference V 0 and the oscilloscope measures the voltage across C 1. The circuit, therefore, is as shown below. 1. Connect the circuit as shown. 5/6

6 μf 2. Set C 2 to 5, flip the DPDT switch from position (1) to position (2), and record the voltage V 1 appearing across C 1 immediately after switching. Repeat the measurement a few times to get a good estimate of its uncertainty. Now change the position of the oscilloscope leads so that they measure the voltage V 2 appearing across C 2 immediately after switching. (We don't show you a figure for this, but by now you shouldn't need another one!) Follow the same procedure as with C Derive an equation giving V 1 and V 2 as a function of C 1, C 2, and V Using the value for C 1 obtained in Part I, does your equation correctly predict the observed voltages? 5. In this circuit, what is the relationship between V 1, V 2, and V 0? phy134/lab3.txt Last modified: 2015/09/17 22:27 (external edit) 6/6