Compacitor

CAPACITANCE

Objective
This lab exercise will define capacitance and demonstrate this definition using a single capacitor in a DC circuit. The size of the capacitor will be measured using ohms law and the definition of capacitance.

Background
A capacitor consists of two flat (large area) conductors placed close together with an insulating material between them - such as two strips of metal foil separated by a thin insulating strip - and then rolled tightly into a small cylinder with an electrode (terminal) connected to each strip. The two strips may then be given opposite charges, and thus charge stored in the capacitor.

Since the strips are charged with opposite charges (+Q, and - Q) a potential difference, V, develops between the two strips. The capacitance of the capacitor, C, is defined as C = Q/V. The charge on the capacitor divided by the potential difference. Since the potential difference depends on the charge of the capacitor, the ratio Q/V remains constant for a given capacitor regardless the amount of charge. That is why defining capacitance is a useful concept. Although a capacitor behaves as a break (or an open circuit) with direct current (dc), initially current will flow to charge the capacitor when a voltage is first applied.

Refer to the circuit diagram shown above. When the switch closes and a voltage is applied across the capacitor plates, current flows to charge the capacitor. The time for the capacitor to charge is very short (in milliseconds) after which the current stops. If the switch is then set to its neutral position disconnecting the battery, the charge remains on the capacitor. If the switch is then set to connect the capacitor to the resistor, the charge will flow from the capacitor through the resistor until the capacitor is discharged. This discharge time may be much longer (in seconds) depending on the size of the resistor. A measure of this current as a function of time will provide a means of obtaining the charge on the capacitor.

Equipment
- capacitor-resistor-switch circuit box
- FLUKE voltmeter

Procedure
1. Use the color code to determine the size of the resistor on your circuit box. Also, read the nominal size of the capacitor as it is printed on the capacitor. Capacitors are measured in farads with typical values in the micro-farad range.

2. Connect the voltmeter to read the potential across the capacitor. (Use the high range) As shown in the circuit diagram, this potential is also the potential of the battery when the battery is connected to the capacitor; and it is also the potential across the resistor when the resistor is connected across the capacitor.

3. Use the three position switch to verify that the voltmeter is correctly connected. Notice that when the switch is positioned for the capacitor to be connected across the resistor, the voltage measurement drops as the capacitor discharges. The procedure of charging the capacitor with the battery and then discharging it through the resistor will be used to determine the current while the capacitor discharged. Practice charging the capacitor with the battery and then discharging it through the resistor while observing the time it takes to discharge. Notice that it will take a very long (infinite) time to completely discharge.

4. You will now measure the voltage drop as a function of time while the capacitor discharges. Since the discharge is a continuous process in which the voltage changes quite rapidly, one cannot expect to take several time and voltage readings while the capacitor discharges. Therefore, the procedure outlined below may be necessary:
a. charge the battery to the battery voltage.
b. start the discharge and a timer at the same time.
c. after a short time, stop the discharge (switch in neutral position) and timer at the same time.
d. record the time and the voltage
e. repeat the above steps to obtain about a dozen values for the discharging process. You should try to get a reading for about every two seconds.

Caution:
When measuring the voltage across the capacitor for the higher voltages, the voltmeter may show a slow decrease in voltage while you are reading the meter. This occurs because the charge on the capacitor is slowly discharging into the air or through the meter. If this occurs you should take the reading as quickly as possible after stopping the discharging process. For lower voltages, the meter may slowly show a slow increase in voltage while you are reading the meter. If this occurs, wait until the meter stops in the third significant figure before the reading is taken.

5. Use Ohm’s Law to calculate the current associated with each voltage reading. Then construct a graph of current as a function of time for the discharging process. Since information will be taken from this graph, it must be at least one half to one full page in size.

6. To determine the amount of charge which flowed off the capacitor as it discharged, one must graphically measure the area under the current/time graph. (Your instructor will explain this process).

7. Calculate the experimental value of the capacitance by C = Q/V (where V is the voltage at time zero.). Compare the experimental value of C with the nominal value printed on the capacitor. Determine the percent difference between these values?

Related Activities
Notice that in the procedure used in this lab, the amount of charge that went on the capacitor was determined by measuring the amount of charge that came off the capacitor while it discharged. Are those two amounts equal? If not; which one would you expect to be greater? Why?