EXERCISE OBJECTIVE
Exercise 3-2
When you have completed this exercise, you will be able to determine the equivalent capacitance for series and parallel capacitors. You will also be able to explain and
demonstrate equivalent capacitance using circuit measurements of current and voltage.
DISCUSSION
Capacitors are electrical devices made up of two parallel conducting plates separated by air, paper, mica, or some other type of material. The separating material is called the dielectric, and different materials have different dielectric constants. This is similar to the fact that different materials have different values for resistivity. Capacitance, like resistance, provides opposition in electric circuits. However, unlike resistance which opposes current flow, capacitance opposes changes in the voltage across the capacitor's terminals. Figure 3-3 illustrates the basic construction of different kinds of capacitors.
Figure 3-3. Construction of Different Types of Capacitors.
A capacitor stores energy in the electric field that is created between its plates when a voltage is applied across them. The amount of energy that a capacitor is able to store depends on its capacitance, which is related to the dielectric constant of the material separating the plates, the size of the plates, and the distance between them. The measurement unit of capacitance, the farad (F), is an extremely large unit, and practical capacitors have values that range in size from picofarads to microfarads. One effective way to increase capacitance is to use a chemical electrolyte between the capacitor plates. This produces a polarized capacitor called electrolytic capacitor. While relatively high values of capacitance are possible with electrolytic capacitors, their polarity must be respected to prevent them from blowing up, often with dangerous explosive force. In all cases capacitors must be treated carefully,
Equivalent Capacitance
tubes. They can store large amounts of energy and may take several days or even weeks to discharge. It is always wise to check that capacitors are discharged before handling them.
When capacitors are connected in series or parallel, the formulas used to determine equivalent capacitance are similar to those used for equivalent resistance. There is a difference however, since the formulas are reversed for capacitance. In parallel combinations, the equivalent capacitance CEQ is greater, while in series
combinations, CEQ is smaller. This is not surprising when you consider that the effect
of several capacitors in parallel is the same as having more plate area in which to store energy. The effect of placing them in series is equivalent to increasing the separation between the plates. This effect is suggested in Figure 3-4.
Figure 3-4. (a) Capacitors in Parallel, (b) Capacitors in Series.
The formula for finding the equivalent capacitance of capacitors in parallel is CEQ'C1+C2+C3+C4+....+CN.
while that for finding the equivalent capacitance of capacitors in series is 1/CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
Rearranging the formula XC' 1 / (2πfC) relating capacitive reactance and
capacitance gives C ' 1 / (2πfXC). This other form can be used to determine circuit
capacitance from measurements of circuit current and voltage.
Equivalent Capacitance
EQUIPMENT REQUIRED
Refer to the Equipment Utilization Chart in Appendix C to obtain the list of equipment required for this exercise.
PROCEDURE
CAUTION!
High voltages are present in this laboratory exercise! Do not make or modify any banana jack connections with the power on unless otherwise specified!
G 1. Install the Power Supply, data acquisition module, and Capacitive Load module in the EMS Workstation.
G 2. Make sure that the main switch of the Power Supply is set to the O (OFF) position, and the voltage control knob is turned fully ccw. Ensure the Power Supply is connected to a three-phase wall receptacle.
G 3. Set up the parallel circuit of Figure 3-5, and connect inputs I1, I2, I3, and E1 as shown. Set the Capacitive Load module for the values of C1, C2, and C3
given in Figure 3-5.
Equivalent Capacitance
G
4. Calculate the equivalent circuit capacitance CEQ using the capacitancevalues given in Figure 3-5.
CEQ' C1 + C2 + C3' μF
G
5. Ensure that the POWER INPUT of the data acquisition module is connected to the main Power Supply, and that the 220vis connected to the data acquisition module.
G 6. Display the Metering application and select setup configuration file
ES13-2.dai.
G 7. Turn on the main Power Supply and set the 24 V - AC power switch to the I (ON) position. Adjust the voltage control to 100 %.
G
8. Use the Record Data button to enter the voltage and current measurements in the Data Table, and note the results below.IC1' A
IC3' A
IC2' A
ES = EC' V
G
9. Use the circuit measurements to determine the capacitance values for C1,C2, and C3. Remember that XC' EC / IC = 1 / (2πfC).
G 10. Do the results of step 9 correspond with the capacitance values set on the Capacitive Load module?
G
YesG
NoG
11. Calculate CEQ using the capacitance values from step 9.3-12
Equivalent Capacitance
G
12. Compare the result of step 11 with the theoretical calculation done in step 4. Are they approximately the same?G
YesG
NoG
13. Turn off the power and set up the circuit of Figure 3-6. Connect inputs I1, E1, E2, and E3 as shown, and set the Capacitive Load module for therequired values of capacitance.
Figure 3-6. Determining Equivalent Capacitance of a Series Circuit.
G 14. Calculate the equivalent circuit capacitance CEQ using the capacitance
values given in Figure 3-6.
CEQ' μF
G
15. Display the Metering application and select setup configuration file ES13-3.dai.Equivalent Capacitance
G
16. Turn on the power and verify that the voltage control is set to 100 %. Measure and record the circuit current and voltages.EC1' V
EC3' V
EC2' V
IS' A
G
17. Use the circuit measurements to determine the capacitance values for C1,C2, and C3.
G
18. Calculate CEQ using the capacitance values from step 17.CEQ' μF
G
19. Compare the result of step 18 with the theoretical calculation done in step 14. Are they approximately the same?G
YesG
No3-14
G
20. Ensure that the Power Supply is turned off, the voltage control is fully ccw, and remove all leads and cables.CONCLUSION
You determined the equivalent circuit capacitance for parallel and series
combinations of capacitors using the formulas for equivalent capacitance. You also combined the use of these formulas with measurements of circuit voltages, currents, and capacitive reactance.
Equivalent Capacitance
REVIEW QUESTIONS
1. What is the formula for determining the equivalent capacitance of a parallel circuit?
a. CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
b. 1/CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
c. CEQ'C1+C2+C3+C4+....+CN.
d. 1/CEQ'C1+C2+C3+C4+....+CN.
2. What is the formula for determining the equivalent capacitance of a series circuit?
a. CEQ'C1+C2+C3+C4+....+CN.
b. 1/CEQ'1/C1+1/C2+1/C3+1/C4+....+1/CN.
c. CEQ'1/(C1+C2+C3+C4+....+CN).
d. 1/CEQ'C1+C2+C3+C4+....+CN.
3. What is the equivalent capacitance of three 15-μF capacitors connected in parallel?
a. 50 μF. b. 4.5 μF. c. 45 μF. d. 5.0 μF.
4. What is the equivalent capacitance of three series-connected capacitors with values of 1 μF, 2 μF, and 4 μF?
a. 7 μF. b. 8 μF. c. 1.75 μF. d. 0.57 μF.
5. What is the equivalent capacitance of two parallel-connected, 10-μF capacitors connected in series with a 5-μF capacitor?
a. 50 μF. b. 25 μF. c. 10 μF. d. 4 μF.