Exercise 2: Inductors in Series and in Parallel
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1 Exercise 2: Inductors in Series and in Parallel EXERCISE OBJECTIVE When you have completed this exercise, you will be able to determine the total inductance of a circuit containing inductors in series and in parallel. You will verify your results with an oscilloscope. DISCUSSION In circuits with more than one inductor, it is often best to determine the total combined inductance. When inductors are in series, total inductance (L T ) is the sum of the inductor values. L T L1 + L2 + L3 Total inductance increases as the number of inductors in series increases. More inductance results in higher impedance and lower circuit current. What is the total inductance (L T ) in the circuit shown below? L T mh (Recall Value 1) For inductors in parallel, the total inductance is, as with resistors, determined from the reciprocal formula, shown below. L T L1 L2 L3 66 FACET by Lab-Volt
2 Inductance L T L1 x L2 L1+ L2 Total inductance decreases as the number of inductors in parallel increases. As more inductors are added in parallel, the impedance is lowered and the circuit current increases. What is the total inductance (L T ) in the above circuit? a. 2 mh b. 4 mh c. 1 mh PROCEDURE If necessary, clear the AC 1 FUNDAMENTALS circuit board of all two-post connectors and any other connections. Adjust V GEN for a 10 V pk-pk sine wave at 20 khz. In the following steps, you will determine the effect on circuit current when an inductor is added in series or in parallel with L3. By observing the single inductor circuit, determine the total inductance (L T ). L T mh (Recall Value 1) FACET by Lab-Volt 67
3 Determine the circuit current (I). NOTE: To determine the ac circuit current, divide the voltage drop across R2 by the resistance of R2 (10 ). V R2 I R2 I ma pk-pk (Recall Value 2) Measure the voltage drop across L3 (V L3 ) with the oscilloscope. V L3 V pk-pk (Recall Value 3) Use your measured values of I ( ma pk-pk [Step 6, Recall Value 2]) and V L3 ( V pk-pk [Step 7, Recall Value 3]) to calculate the impedance of L3 (Z L3 ). Z L3 V I L3 Z L3 (Recall Value 4) 68 FACET by Lab-Volt
4 Inductance (essentially adding an inductor in series). Adjust V GEN for a 10 V pk-pk sine wave at 20 khz. Determine the total inductance (L T ). L T L1 + L2 L T mh (Recall Value 5) Did adding the inductor in series increase or decrease total circuit inductance (L T )? a. increase b. decrease Determine the circuit current (I). NOTE: To determine the ac circuit current, remove the two-post connector and use the oscilloscope to measure the peak-to-peak voltage drop across R2. Take the measurement and divide the value by the resistance of R2 (10 ). Replace the two-post connector before moving on to the next step. I V R2 R2 I ma pk-pk (Recall Value 6) FACET by Lab-Volt 69
5 Measure the combined voltage drops across L1 and L2 (V LT ) with the oscilloscope. V LT V pk-pk (Recall Value 7) Use your measured values of I ( ma pk-pk [Step 13, Recall Value 6]) and V LT ( V pk-pk [Step 14, Recall Value 7]) to calculate the combined impedance of L1 and L2 (Z LT ). Z LT V I LT Z LT (Recall Value 8) Compare your data (recalled below) from the two circuits. Which circuit offers the greatest GEN )? a. single inductor circuit b. two-inductor series circuit Single inductor circuit L T 4.70 mh Two-inductor series circuit L T 9.40 mh I ma pk-pk (Step 6, Recall Value 2) I ma pk-pk (Step 13, Recall Value 6) Z L3 (Step 8, Recall Value 4) Z LT (Step 15, Recall Value 8) Connect the circuit shown. An inductor (L4) is added in parallel with L3. Adjust V GEN for a 10 V pk-pk sine wave at 20 khz. 70 FACET by Lab-Volt
6 Inductance In the following steps, you will determine the effect on circuit current when an inductor is added in parallel with L3. Determine the total inductance (L T ). L T L1 x L2 L1+ L2 L T mh (Recall Value 9) Determine the circuit current (I) by using current-sensing resistor R2. V R2 I R2 I ma pk-pk (Recall Value 10) FACET by Lab-Volt 71
7 Measure the voltage drop across parallel inductors L3 and L4 (V L ). V L V pk-pk (Recall Value 11) Use your measured values of I ( ma pk-pk [Step 20, Recall Value 10]) and V L ( V pk-pk [Step 21, Recall Value 11]) to calculate the combined parallel impedance of L3 and L4 (Z L ). VL ZL I Z L (Recall Value 12) Compare your data (recalled below) from the two circuits. Which circuit offers the greatest GEN )? a. single inductor circuit b. two-inductor parallel circuit Single inductor circuit L T 4.70 mh Two-inductor series circuit L T 9.40 mh I ma pk-pk (Step 6, Recall Value 2) I ma pk-pk (Step 20, Recall Value 10) Z L3 (Step 8, Recall Value 4) Z LT (Step 22, Recall Value 12) Monitor the circuit current on the oscilloscope by observing the amplitude of the voltage across current-sensing resistor R2. 72 FACET by Lab-Volt
8 Inductance Place CM switch 17 in the ON position to add an unseen inductor to the circuit. While observing the oscilloscope, toggle the CM switch off and on. Based on the circuit s current change, was the new inductor added to the circuit in series or in parallel with L3 and L4? a. series b. parallel Make sure all CMs are cleared (turned off) before proceeding to the next section. CONCLUSION The total inductance of inductors in series is the sum of the individual inductor values. To determine total inductance of inductors in parallel, use the reciprocal method. The more inductors added in series, the higher the inductance and impedance, and the lower the circuit current. The more inductors added in parallel, the lower the inductance and impedance, and the higher the circuit current. REVIEW QUESTIONS 1. The total inductance of inductors in series is a. determined from the reciprocal method. b. the sum of the inductor values divided by two. c. the sum of the inductor values. d. the reciprocal of the sum of the inductors. 2. The total inductance of inductors in parallel is a. determined from the reciprocal method. b. the sum of the inductor values. c. the sum of the inductor values divided by two. d. the reciprocal of the sum of the inductors. 3. As more inductors are added in parallel, a. circuit current increases. b. impedance increases. c. circuit current decreases. d. inductance increases. 4. As more inductors are added in series, a. inductance decreases. b. circuit current increases. c. circuit current decreases. d. impedance decreases. FACET by Lab-Volt 73
9 5. GEN for a 10 V pk-pk, 20 khz sine wave. Monitor the circuit current on the oscilloscope by observing the amplitude of the voltage across current-sensing resistor R2. Place CM switch 16 in the ON position to add an unseen inductor to the circuit. Toggle CM 16 off and on. Based on the circuit current change, the unseen inductor a. was added in parallel. b. had no effect on circuit current. c. was added in series. d. caused the circuit current to increase. NOTE: Make sure all CMs are cleared (turned off) before proceeding to the next section. 74 FACET by Lab-Volt
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