EXERCISE OBJECTIVE
Exercise 4-2
When you have completed this exercise, you will be able to determine the equivalent inductance for series and parallel inductors. You will also be able to explain and
demonstrate equivalent inductance using circuit measurements of current and voltage.
DISCUSSION
Inductors are electrical devices made up of a coil of wire wound around a core. The core material can be non-magnetic like wood or plastic, or magnetic material like iron or steel. Inductors made with non-magnetic cores are called air-core inductors, while those with iron and steel are iron-core inductors. Using magnetic materials for the core allows greater values of inductance to be obtained because magnetic materials concentrate the magnetic lines of force into a smaller area. Figure 4-3 shows examples of air-core and iron-core inductors.
Figure 4-3. (a) Air-Core Inductor, (b) Iron-Core Inductor.
An inductor stores energy in the magnetic field created around its coil of wire when the current through the coil changes. The amount of energy that the inductor can store depends on its inductance, the type of core and the number of turns of wire. The measurement unit for inductance, the henry (H), is the value obtained when current changing at a rate of one ampere per second causes a voltage of one volt to be induced in the inductor.
Equivalent Inductance
Figure 4-4. Inductors in Series.
4-10
The formulas used to determine equivalent inductance are the same form as those used for equivalent resistance. As in the case for resistance, equivalent inductance LEQ is greater for series-connected inductors, while it is smaller for parallel
combinations. Series and parallel combinations of inductors are shown in Figures 4-4 and 4-5, respectively.
Figure 4-5. Inductors in Parallel.
The formula for finding the equivalent inductance of inductors in series is LEQ'L1+L2+L3+L4+....+LN.
while that for finding the equivalent inductance of inductors in parallel is 1/LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
Rearranging the formula XL' 2πfL relating inductive reactance and inductance gives
L ' XL / (2πf). This other form can be used to determine circuit inductance from
Equivalent Inductance
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 Inductive 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 4-6, and connect inputs I1, I2, I3, and E1 as shown. Set the Inductive Load module for the values of L1, L2, and L3
given in Figure 4-6.
Equivalent Inductance
G
4. Calculate the equivalent circuit inductance LEQ using the inductance valuesgiven in Figure 4-6.
LEQ' H
G 5. Ensure that the POWER INPUT of the data acquisition module is connected to the main Power Supply, and that the power cable
is connected to the data acquisition module.
G 6. Display the Metering configure configuration
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.IL1' A
IL3' A
IL2' A
ES' V
G
9. Use the circuit measurements to determine the inductance values for L1, L2,and L3. Remember that XL' ES / IL = 2πfL.
G 10. Do the results of step 9 correspond with the inductance values set on the Inductive Load module?
4-12
Equivalent Inductance
G
11. Calculate LEQ using the inductance values from step 9.LEQ' H
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 4-7. Connect inputs I1, E1, E2, and E3 as shown, and set the Inductive Load module for therequired values of inductance.
Figure 4-7. Determining Equivalent Inductance of a Series Circuit.
G 14. Calculate the equivalent circuit inductance LEQ using the inductance values
given in Figure 4-7.
Equivalent Inductance
G
15. Display the Metering screen and select setup configuration file ES14-3.dai.G 16. Turn on the power and verify that the voltage control is set to 100 %. Measure and record the circuit current and voltages.
EL1' V
EL3' V
EL2' V
IS' A
G
17. Use the circuit measurements to determine the inductance values for L1, L2,and L3.
G
18. Calculate LEQ using the inductance values from step 17.LEQ' L1 + L2 + L3' H
G 19. Compare the result of step 18 with the theoretical calculation done in step 14. Are they approximately the same?
G
YesG
No4-14
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 inductance for parallel and series combinations of inductors using the formulas for equivalent inductance. You also combined the use of these formulas with measurements of circuit voltages, currents, and inductive reactance.
Equivalent Inductance
REVIEW QUESTIONS
1. What is the formula for determining the equivalent inductance of parallel- connected inductors?
a. LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
b. 1/LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
c. LEQ'L1+L2+L3+L4+....+LN.
d. 1/LEQ'L1+L2+L3+L4+....+LN.
2. What is the formula for determining the equivalent inductance of series- connected inductors?
a. LEQ'L1+L2+L3+L4+....+LN.
b. 1/LEQ'1/L1+1/L2+1/L3+1/L4+....+1/LN.
c. LEQ'1/(L1+L2+L3+L4+....+LN).
d. 1/LEQ'L1+L2+L3+L4+....+LN.
3. What is the equivalent inductance of three 15-H inductors in parallel? a. 50 H.
b. 4.5 H. c. 45 H. d. 5.0 H.
4. What is the equivalent inductance of three series-connected inductors with values of 1 H, 2 H, and 4 H?
a. 7 H. b. 8 H. c. 1.75 H. d. 0.57 H.
5. What is the equivalent inductance of two parallel-connected, 10-H inductors connected is series with a 5-H inductor?
a. 50 H. b. 25 H. c. 10 H. d. 5 H.