Capacitor-Resistor Lab

Tim the Tool Man Taylor wants to rig his car stereo so that when he turns on his car, his stereo blasts out the sound immediately. In order to do this, he will attach a capacitor which will supply a burst of extra power immediately. His wife, Jill, warns him that he must first measure the power from a capacitor, so he does not blow anything up. Tim has already met his quota of blowing up things this week, so he seeks someone to measure the power for him. He knows the excellent reputation of students in our school, so he asks our class collect the data he needs. He sent something for your efforts.

1. Place your calculator in the cradle of the CBL2 and make sure the short link cable is connecting the two.

2. Connect the voltage cable to Ch1 on the side of the CBL

3. Connect the red lead to the positive side of the capacitor and the black side to the negative. An arrow on the capacitor shows the direction of flow from positive to negative.

4. Press the APPS button on your calculator and select DATAMATE.

5. To caliber (zero) the voltage, select SETUP and press 3:ZERO. Select 1:CH1-VOLTAGE(V) and press [ENTER]

6. The CBL should automatically detect the voltage probe and give you a Mode: Time Graph – 18 setting. This means it will collect voltage for 18 seconds (usually at 0.1 second intervals).

7. Place the positive lead of the wires on the positive lead of the 9 volt battery and the negative on the negative. (If you have set this up right, on the screen of the CBL the voltage should be showing near the upper right corner.)

8. Press the number 2 (Start) on the calculator and immediately remove the leads from the battery. The CBL should beep and begin displaying the graph of the changing voltage.

9. Don’t touch anything for the 18 seconds of collection time. At the end of this time the CBL will re-graph the data in a better window.

10. Press ENTER.

11. Press 6.

12. Press ENTER.

You should now be out of the program.

Link lists 1 and 2 to your partner, set up a STAT PLOT and use ZOOM 9 to see the graph. (Remember to turn off or clear functions in Y=.)

Go to the modeling page to analyze the data.

Analysis of Data

1) Sketch your graph of the data below. Label scales and axes. Is this a decay or growth graph?

2) By trial and error find an exponential equation of the form where v is voltage and t is time. Place the equation in y1 and graph it with the STAT PLOT.

Y1 = _________________

3) We can also model this by using half-life. Half-life is the amount of time it takes for half of a quantity to decay. By tracing on your data, find how long it took for the capacitor to lose half its charge. Record it as “h” below. Then make y2 the equation and graph y2 over the data.

h = _______________ Y2 = _________________

In your opinion, does this provide a better or worse fit than trial and error? What makes you say that?

To the best of your ability, explain why the given equation works. Think in terms of what happen every h seconds.

(over)

4) We will now fit the data using where e is the constant mentioned in section 3.1 and k is a constant of decay. K is determined by the equation where R is the rating of the resistor in Ohms and C is the rating of the capacitor in farads. In our experiment the capacitor rating was 220 mF (micro farads) and the resistor rating was 100 k-Ohms. Place the equation in y3 and graph it. Turn off y1 since the screen is probably getting cluttered.

k = __________ Y3 = _________________

5) Finally, do an exponential regression with your calculator and place the resulting equation in y4. Graph it as well.

Y4 = _____________________

For the stars!

Show algebraically, how the equations , , and are all really

the same equation, just in different forms.

Created by G. Hill

Modified by C. Baker 8/02