Purpose of this Minilab

1. Purpose of this Minilab • Learn about charging and discharging of a capacitor through a resistor. • Learn how to build a simple resistor and capacitor from “everyday materials”.

2. What is a “Capacitor”? Capacitor = an object that can store electric charge Q. Example: Two metal plates + - - + - + - + - + - - + + - +

3. What is a “Capacitor”? Relationship between charge and voltage Total charge on one plate: Q + - - + - + - + - + - - + + - + Capacitance of the capacitor Voltage V

4. Getting the Charge on the Capacitor Current (movement of charge) must occur: Applying a voltage will cause current to flow when switch is closed. C not charged…yet switch battery/power supply R resistance of circuit e

5. Getting the Charge on the Capacitor Voltage across capacitor is increasing as more charge is deposited. has opposite polarity compared to e. + - + - + - I I Current decreases as charge increases on the capacitor. - + I I e

6. Getting the Charge on the Capacitor + - - + - + - + - + - + + - Capacitor is fully charged  No more current flows - + I = 0 e

7. The Charging Process …Mathematically I t Q V t

8. Discharging the Capacitor Removing battery and closing the loop: Voltage across capacitor is decreasing as charge is leaving. + - + - + - I I Current decreases as charge decreases on the capacitor. - + I I

9. The Discharging Process …Mathematically I Note: Current flows in opposite direction compared to charging. t Q V t

10. The “RC time constant” The product RC has units of time: It is called the “time constant of the RC circuit”. For the discharging process we saw: initial voltage of the capacitor at time t=0 (start of discharge) so…after a time t=RC has elapsed…..

11. Measuring the “RC time constant” During the Discharge Process V Vinitial Vinitial*0.368 t RC Note: Your initial voltage can be at ANY starting point.

12. The “RC time constant” For the charging process we saw:  and…after a time t=RC has elapsed….. And the final (maximum) voltage is reached after a “long” time…

13. Measuring the “RC time constant” During the Charging Process Vcapacitor Vfinal Vfinal*0.63 t RC Note: Your initial voltage must be 0.

14. Using the Function Generator to Automate Charging and Discharging C R V Must use thesquare wave of function generator

15. C R V Measuring Vcapacitor(t) with the Oscilloscope Oscilloscope

16. Connections Oscilloscope C R Function Generator The black cables clips must be located as shown!

17. Power remains OFF on breadboard in this lab. To Oscilloscope To Function Generator

18. A Close View To Oscilloscope Capacitor Resistor Both black clips must be attached to the same point in circuit. To Function Generator

19. Choosing a Good Frequency on Function Generator Period (T) Function Generator Voltage time Capacitor discharges Capacitor charges Capacitor discharges Capacitor charges • Theoretical charge time = RC • Period (T) should be approximately 10*RC so that capacitor can fully charge and discharge. frequency (=1/T) should be approximately 1/(10*RC)

20. If Frequency is Chosen Well ….Oscilloscope Will Show …. Oscilloscope (Vcapacitor) time Capacitor discharges Capacitor charges Capacitor charges Capacitor discharges

21. Frequency too High ….. Oscilloscope (Vcapacitor) time Not enough time for proper charging and discharging:  Looks like sawtooth

22. Frequency too Low  Harder to Measure RC Oscilloscope (Vcapacitor) time Capacitor discharges Capacitor charges Capacitor discharges Capacitor charges

23. Choose Oscilloscope Channel 1 Mode = DC First push “Ch1 Menu” Button Then select coupling With this button (must be “DC”).

24. Vmax Hints for Measuring RC with Oscilloscope * Use the cursor functions to measure voltages and time differences. * Expand x and y axes to get good resolution. 0.63 Vmax RC

25. The Capacitance Meter Small knob can be turned to “zero” capacitance meter.

26. Using Capacitance Meter with Clips • First position leads • where you want them. • 2) “Zero” capacitance • meter without • capacitor attached. • 3) Attach capacitor but • try to move leads as • little as possible.

27. Using Capacitance Meter without Clips • Remove leads. • 2) “Zero” capacitance • meter without • capacitor attached. • 3) Insert capacitor into • slits as shown.

28. Making a Resistor from Paper and Carbon White cardboard Use alligator clips to make good electric contact. Draw with pencil (apply thick layer).

29. Measuring R If you deposit a generous thickness of carbon, about as large as shown, you should get approx. 100kW resistance. If you get a few MW, you need to apply carbon more thickly with the pencil.

30. Varying Length (L) and Area (A) of Resistor L Simply attach clips at different positions to vary L. W Varying W effectively changes A (A=W*Thickness of carbon)  Draw broader W for more A.

31. Making a Capacitor 8”x11” paper Aluminum foil smaller than paper (but not much smaller). Keep Aluminum foil as flat as possible. Leave overhang for clips

32. Step-by-Step 1 2 3 4 5 The two aluminum foils must not touch each other anywhere. (Separate them with a sheet of paper). Put a heavy book on top to keep aluminum foil as flat as possible. Use the overhangs to make electric connection with alligator clips.

33. Varying the Capacitance Area of capacitor (in our case this is the area of overlap of the two aluminum foils). Distance between the aluminum foils ( = thickness of paper).

34. Varying the Capacitance Change “d” by inserting 1, 2, 3… sheets of paper between the two foils (doubles, triples, etc. “d”). You can simply move one sheet to change the area of overlap. Effective area of overlap. Make sure to cover with book again!!