Exercise 1: Series RLC Circuits
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1 RLC Circuits AC 2 Fundamentals Exercise 1: Series RLC Circuits EXERCISE OBJECTIVE When you have completed this exercise, you will be able to analyze series RLC circuits by using calculations and measurements. You will verify your results with an oscilloscope. DISCUSSION T ) in a series RLC circuit is a combination of the oppositions offered by the resistance (R), inductive reactance (X L ), and capacitive reactance (X C ). Net reactance is the difference between the two reactances. An RLC circuit can be reduced to one equivalent resistance and one net reactance (X NET ). When the value of capacitive reactance (X C ) is larger than the value of inductive reactance (X L ), the circuit acts like a resistor in series with an equivalent capacitor. The net reactance is determined as follows: X CNET = X C X L 10 FACET by Lab-Volt
2 AC 2 Fundamentals RLC Circuits However, when the value of inductive reactance (X L ) is larger than the capacitive reactance (X C ), the circuit acts like a resistor in series with an equivalent inductor. The net reactance is determined as follows: X LNET = X L X C This series RLC circuit acts like a 100 resistor in series with an equivalent a. capacitor. b. inductor. Knowing the reactances and resistance of a series RLC circuit, you can calculate the total circuit impedance (Z) C1 L1 Z = R + ( X X ) Z= 2565 FACET by Lab-Volt 11
3 RLC Circuits AC 2 Fundamentals Using the values of Z and V GEN, you can calculate the total circuit current from Ohm s law. Now that you know circuit current, you can calculate the voltage drop across each component by using Ohm s law. V R1 = I T x R1 = 5.85 x 10 3 x 1000 = 5.85 V V L1 = I T x X L1 = 5.85 x 10 3 x 1256 = 7.35 V 12 FACET by Lab-Volt
4 AC 2 Fundamentals RLC Circuits V C1 = I T x X C1 = 5.85 x 10 3 x 3619 = 21.2 V In a series RLC circuit, does the sum of the component voltage drops equal the applied source voltage (V GEN )? a. yes b. no The following equation is used to determine V GEN, where V R equals the total resistive voltage drop and V NET equals the net reactive voltage (V C1 V L1 ). 2 2 GEN = R + NET V V V FACET by Lab-Volt 13
5 RLC Circuits AC 2 Fundamentals Calculate V GEN. ( ) 2 2 GEN = R1 + C1 L1 V V V V V GEN = V pk-pk (Recall Value 1) This phasor diagram shows the relationship of the voltage drops of the resistive and reactive components to the source voltage (V GEN ). V GEN does not equal the sum of the voltage drops across the individual components. ( ) 2 2 GEN = R1 + C1 L1 V V V V 14 FACET by Lab-Volt
6 AC 2 Fundamentals RLC Circuits A practical way to tell if an RLC is inductive or capacitive is to measure the individual voltage drops across the inductor and capacitor. The one with the highest voltage drop determines the total reactive effect. This circuit acts like a resistor in series with an equivalent a. inductor. b. capacitor. The impedance phase angle ( ) can be determined from the following equation, where X NET equals (X L X C ) or (X C X L ). θ = tan X R 1 NET FACET by Lab-Volt 15
7 RLC Circuits AC 2 Fundamentals When the voltage drop across each component is known, you can determine the phase angle ( ) from the following equation, where V NET equals (V L1 V C1 ) or (V C1 V L1 ). θ = tan V V 1 NET R1 Calculate the phase angle ( ) in the series RLC circuit shown above. θ = tan V V 1 NET R1 = degrees (Recall Value 2) Circuit values depend upon the frequency of the applied voltage. Changing the frequency changes the reactive values and other factors in the circuit. Increasing the frequency increases the value of inductive reactance and lowers the value of capacitive reactance. Decreasing the frequency decreases the value of inductive reactance and raises the value of capacitive reactance. Changing the frequency changes the way a circuit acts (either inductively, capacitively, or resistively). PROCEDURE Adjust (V GEN ) for a 15 V pk-pk, 20 khz sine wave. Set the frequency and amplitude with the oscilloscope. 16 FACET by Lab-Volt
8 AC 2 Fundamentals RLC Circuits In the next few steps, you will measure the voltage drops across the individual components. You will compare the value of generator voltage (V GEN ) with the individual voltage drops. 2 2 GEN = R + NET V V V Connect the oscilloscope as shown, and measure the voltage drop across C1 (V C1 ). V C1 = V pk-pk (Recall Value 1) Connect the oscilloscope as shown, and use the ADD-INVERT method to measure the voltage drop across L1 (V L1 ). V L1 = V pk-pk (Recall Value 2) FACET by Lab-Volt 17
9 RLC Circuits AC 2 Fundamentals Connect the oscilloscope as shown, and use the ADD-INVERT method to measure the voltage drop across R2 (V R2 ). V R2 = V pk-pk (Recall Value 3) Compare the value of V GEN (15 V pk-pk ) with your measured values of V C1 ( V pk-pk [Step 3, Recall Value 1]), V L1 ( V pk-pk [Step 4, Recall Value 2]), and V R2 ( V pk-pk [Step 5, Recall Value 3]). In a series RLC circuit, is the applied voltage (V GEN ) equal to the sum of the individual component drops? a. yes b. no In the following steps, you will determine if this circuit acts inductively or capacitively at an input frequency of 20 khz. You will increase the value of C1 and observe any changes in circuit performance. Compare your measured values of V C1 and V L1. V C1 = V pk-pk (Step 3, Recall Value 1) V L1 = V pk-pk (Step 4, Recall Value 2) This circuit acts like a resistor in series with an equivalent a. capacitor. b. inductor. 18 FACET by Lab-Volt
10 AC 2 Fundamentals RLC Circuits Connect the oscilloscope channels as shown. Observe the phase angle ( ) between the circuit current (circuit current and V R3 have identical phase) and the applied generator voltage (V GEN ). Use V GEN as the reference. Does the circuit current lead or lag the applied generator voltage? a. lead b. lag Place CM switch 10 in the ON position to increase the value of C1. Observe the voltage drops across L1 and C1. Does this circuit change cause the circuit to be inductive or remain capacitive? a. capacitive b. inductive In the following steps, you will determine if this circuit acts inductively or capacitively at an input frequency of 50 khz. You will calculate the circuit phase angle ( ). FACET by Lab-Volt 19
11 RLC Circuits AC 2 Fundamentals Adjust V GEN for a 15 V pk-pk, 50 khz sine wave. Set the frequency and amplitude with the oscilloscope. Connect the oscilloscope as shown, and measure the voltage drop across C1 (V C1 ). V C1 = V pk-pk (Recall Value 4) Connect the oscilloscope as shown, and use the ADD-INVERT method to measure the voltage drop across L1 (V L1 ). V L1 = V pk-pk (Recall Value 5) Connect the oscilloscope as shown, and use the ADD-INVERT method to measure the voltage drop across R2 (V R2 ). V R2 = V pk-pk (Recall Value 6) 20 FACET by Lab-Volt
12 AC 2 Fundamentals RLC Circuits Compare your measured values of V C1 and V L1. V C1 = V pk-pk (Step 12, Recall Value 4) V L1 = V pk-pk (Step 13, Recall Value 5) This circuit acts like a resistor in series with an equivalent a. capacitor. b. inductor. Using the voltage drop across each component, calculate the phase angle ( ). V C1 = V pk-pk (Step 12, Recall Value 4) V L1 = V pk-pk (Step 13, Recall Value 5) V R2 = V pk-pk (Step 14, Recall Value 6) θ = tan V V V 1 L1 C1 R2 = degrees (Recall Value 7) Connect the oscilloscope channels as shown. Observe the phase angle ( ) between the circuit current (circuit current and V R3 have identical phase) and the applied generator voltage (V GEN ). Use V GEN as the reference. FACET by Lab-Volt 21
13 RLC Circuits AC 2 Fundamentals Does the circuit current lead or lag the applied generator voltage? a. lead b. lag Make sure all CMs are cleared (turned off) before proceeding to the next section. CONCLUSION As frequency varies in a series RLC circuit, the reactances, impedance, voltage, current, and phase angle change. At lower frequencies, X C is greater than X L, so the circuit acts capacitively and the current leads the voltage. At higher frequencies, X L is greater than X C, so the circuit acts inductively and the current lags the voltage. The sum of the component voltage drops does not equal the applied source voltage because the voltages are out of phase with one another. REVIEW QUESTIONS 1. GEN for a 15 V pk-pk, 20 khz sine wave. Set the frequency and amplitude with the oscilloscope. Place the CM switch 11 in the ON position to decrease the value of C1. Connect the oscilloscope channels as shown. Use V GEN as the reference. Observe the phase angle ( ) between the circuit current and the V GEN. 22 FACET by Lab-Volt
14 AC 2 Fundamentals RLC Circuits While observing the phase angle ( ), toggle CM switch 11 off and on. Based on your observation of the phase angle ( ), you determine that the CM caused the circuit to a. change from capacitive to inductive. b. remain inductive. c. change from inductive to capacitive. d. remain capacitive. 2. A series RLC circuit acts like a resistor in series with an inductor when a. X C is greater than X L. b. X L is less than X C. c. V L is greater than V C. d. V C is greater than V L. 3. Based on the given values, the circuit acts a. resistively. b. like an inductor is in series with a capacitor. c. like a resistor is in series with an inductor. d. like a resistor is in series with a capacitor. 4. In this series RLC circuit, V C is greater than V L. The current a. lags the applied voltage. b. leads the applied voltage. c. and voltage are in phase. d. and voltage phase relationship cannot be determined with this data. 5. In a series RLC circuit, the component voltage drops a. equal the applied source voltage. b. are in phase with one another. c. are out of phase with one another. d. can be added directly. NOTE: Make sure all CMs are cleared (turned off) before proceeding to the next section. FACET by Lab-Volt 23
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