Lab 4: Phasors and AC Power

ECE202 - Electrical Circuits I

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1 Objectives

In this fourth lab session, you will continue to use the CircuitJS simulator to experiment with simple passive circuits to test and confirm the validity of the AC circuit theory you have been taught in the lectures. The objectives are as follows:

Introduce the following concepts:

• Phasors
• Active, Reactive and Apparent Power
• Power Factor
• Power Triangle
• RLC series circuit
• RC parallel circuit

1.1 Equipment Required

• Lab 4 - Results sheet to record your measurements.
• Computer with an compatible browser.
• CircuitJS (aka. Falstad Circuit Simulator).

1.2 Background

• Phasor Diagrams and Phasor Algebra
• Complex Numbers and Phasors
• Reactive Power
• Power in AC Circuits
• Power Triangle and Power Factor
• Series RLC Circuit Analyses
• Parallel RLC Circuit Analyses

2 Procedures

2.1 Individual Components

1. Follow along with this video to create and simulate the circuit as shown below:

   

   figure 1. Individual components schematic

2. Use this link to start a blank CircuitJS simulation.

   • V1 = 5V^PEAK @ 40 Hz
   • R1 = 1.0kΩ
   • L1 = 3.98H = 1.0kΩ @ 40Hz - set V1 phase to 90° to avoid a DC offset current.
   • C1 = 3.98uF = 1.0kΩ @ 40Hz - need to add small 1Ω resistor to circuit in order to simulate.

3. Use the tools in CircuitJS to measure the following for the 3 individual circuits created in the video, record all of the following measurements in the appropriate place on your results sheet:

   • V^MAX (V) - Measure the maximum voltage using the scope.

   • V^MIN (V) - Measure the minimum voltage using the scope.

   • V^RMS (V) - Measure using the scope or calculate from the peak value.

   • I^MAX (mA) - Measure the maximum current using the scope.

   • I^MIN (mA) - Measure the minimum current using the scope.

   • I^RMS (mA) - Measure using the scope or calculate from the peak value.

   • R/X_L/X_C (Ω) - Calculate the resistance/reactance from your measured voltage and current.

   • t1_(VMAX) (ms) - Measure the simulation time at maximum voltage.

   • t2_(VMAX) (ms) - Measure the simulation time at next cycles maximum voltage.

   • period (ms) - Calculate the period from t2_(VMAX) - t1_(VMAX).

   • frequency (Hz) - Calculate from the measured period above.

   • t3_(IMAX) (ms) - Measure time at the maximum current closest to t1_(VMAX).

   • I (lead/lag) V - Indicate if the current leads, lags or is in-phase with the voltage.

   • t_phase (ms) - Calculate the difference in time from t3_(IMAX) - t1_(VMAX).

   • phase (°) - Calculate the phase of the current relative to the voltage from t_phase and period.

   • P^MAX (mW) - Measure the peak power using the ‘Show Power Consumed’ and ‘Show Peak Value’ on the scope.

   • P^AVERAGE (mW) - Measure the average power using the ‘Show Power Consumed’ and ‘Show Average’ on the scope.

   • P^MIN (mW) - Measure the negative peak power using the ‘Show Power Consumed’ and ‘Show Negative Peak Value’ on the scope.

2.2 Series RLC

4. To experiment with how passive components behave in a circuit we are first going to look at a simple RLC series circuit. We are going to supply the circuit with an AC voltage supply and change the frequency to see how the circuit and components behave. We will look at the voltage and current magnitudes in each circuit component as well as their phases. We will also look at the instantaneous power in each of the components to see how power behaves in the circuit. Use the CircuitJS link under the schematic to start your circuit simulation and use the simulators tool, which have been demonstrated in the videos, to collect the required measurements.

figure 2. Series RLC circuit
Click here to run this circuit in CircuitJS.

5. Measure and calculate the following magnitudes and phases:

   • V₁^MAX (V) - Measure the maximum supply voltage using the scope.

   • t1_(V1MAX) (us) - Measure the simulation time at the maximum supply voltage.

   • t2_(V1MAX) (us) - Measure the simulation time at the next cycles maximum supply voltage.

   • period (us) - Calculate the period from t2_(V1MAX) - t1_(V1MAX).

   • freq (kHz) - Calculate from the measured period above.

   • I1^MAX (mA) - Measure the maximum current using the scope.

   • t_(I1MAX) (us) - Measure the simulation time at the maximum current closest to t1_(V1MAX).

   • I1 (lead/lag) V1 - Indicate if the current (I1) leads, lags or is in-phase with the voltage (V1).

   • I1 phase (°) - Calculate the phase of the current relative to the supply voltage from t1_(V1MAX), t_(I1MAX) and period.

   • V_C^MAX (V) - Measure the maximum voltage across the capacitor using the scope.

   • t_(VCMAX) (us) - Measure the simulation time at the maximum voltage across the capacitor closest to t1_(V1MAX).

   • V_C (lead/lag) V1 - Indicate if the voltage (V_C) leads, lags or is in-phase with the voltage (V1).

   • V_C phase (°) - Calculate the phase of V_C relative to the supply voltage from t1_(V1MAX), t_(VCMAX) and period.

   • V_L^MAX (V) - Measure the maximum voltage across the inductor using the scope.

   • t_(VLMAX) (us) - Measure the simulation time at the maximum voltage across the inductor closest to t1_(V1MAX).

   • V_L (lead/lag) V1 - Indicate if the voltage (V_L) leads, lags or is in-phase with the voltage (V1).

   • V_L phase (°) - Calculate the phase of V_L relative to the supply voltage from t1_(V1MAX), t_(VLMAX) and period.

   • V_R^MAX (V) - Measure the maximum voltage across the resistor using the scope.

   • t_(VRMAX) (us) - Measure the simulation time at the maximum voltage across the resistor closest to t1_(V1MAX).

   • V_R (lead/lag) V1 - Indicate if the voltage (V_R) leads, lags or is in-phase with the voltage (V1).

   • V_R phase (°) - Calculate the phase of V_R relative to the supply voltage from t1_(V1MAX), t_(VRMAX) and period.

6. Measure and calculate the following power quantities:

   • P_V1^AVERAGE (mW) - Measure the average power supplied to the circuit using the ‘Show Power Consumed’ and ‘Show Average’ on the supply scope.

   • P_C^AVERAGE (mW) - Measure the average power consumed by the capacitor using the ‘Show Power Consumed’ and ‘Show Average’ on the capacitors scope.

   • P_L^AVERAGE (mW) - Measure the average power consumed by the inductor using the ‘Show Power Consumed’ and ‘Show Average’ on the inductors scope.

   • P_R^AVERAGE (mW) - Measure the average power consumed by the resistor using the ‘Show Power Consumed’ and ‘Show Average’ on the resistors scope.

   • P_V1 (mW) - Calculate the circuits real power consumption by using the supply voltage, supply current and phase measurement.

   • Q_V1 (mVAR) - Calculate the circuits reactive power consumption by using the supply voltage, supply current and phase measurement.

   • S_V1 (mVA) - Calculate the circuits apparent power consumption by using the supply voltage, supply current and phase measurement.

   • PF (-) - Calculate the circuits Power Factor.

2.3 Parallel RC

7. Continue experimenting with how passive components behave in a circuit by simulating a Parallel RC circuit. We are going to supply the circuit with an AC voltage supply and change the frequency to see how the circuit and components behave. We will look at the voltage and current magnitudes in each circuit component as well as their phases. We will also look at the instantaneous power in each of the components to see how power behaves in the circuit. Use the CircuitJS link under the schematic to start your circuit simulation and use the simulators tool, which have been demonstrated in the videos, to collect the required measurements.

figure 3. Parallel RC circuit
Click here to run this circuit in CircuitJS.

8. Measure and calculate the following magnitudes and phases:

   • V₁^MAX (V) - Measure the maximum supply voltage using the scope.

   • t1_(V1MAX) (ms) - Measure the simulation time at the maximum supply voltage.

   • t2_(V1MAX) (ms) - Measure the simulation time at the next cycles maximum supply voltage.

   • period (ms) - Calculate the period from t2_(V1MAX) - t1_(V1MAX).

   • freq (Hz) - Calculate from the measured period above.

   • I1^MAX (mA) - Measure the maximum current using the scope.

   • t_(I1MAX) (ms) - Measure the simulation time at the maximum current closest to t1_(V1MAX).

   • I1 (lead/lag) V1 - Indicate if the current (I1) leads, lags or is in-phase with the voltage (V1).

   • I1 phase (°) - Calculate the phase of the supply current relative to the supply voltage from t1_(V1MAX), t_(I1MAX) and period.

   • I_C^MAX (mA) - Measure the maximum current through the capacitor using the scope.

   • t_(ICMAX) (ms) - Measure the simulation time at the maximum current through the capacitor closest to t1_(V1MAX).

   • I_C (lead/lag) V1 - Indicate if the current (I_C) leads, lags or is in-phase with the voltage (V1).

   • I_C phase (°) - Calculate the phase of the capacitor current relative to the supply voltage from t1_(V1MAX), t_(ICMAX) and period.

   • I_R^MAX (mA) - Measure the maximum current through the resistor using the scope.

   • t_(IRMAX) (ms) - Measure the simulation time at the maximum current through the resistor closest to t1_(V1MAX).

   • I_R (lead/lag) V1 - Indicate if the current (I_R) leads, lags or is in-phase with the voltage (V1).

   • I_R phase (°) - Calculate the phase of the resistor current relative to the supply voltage from t1_(V1MAX), t_(IRMAX) and period.

9. Measure and calculate the following power quantities:

   • P_V1^AVERAGE (mW) - Measure the average power supplied to the circuit using the ‘Show Power Consumed’ and ‘Show Average’ on the supply scope.

   • P_C^AVERAGE (mW) - Measure the average power consumed by the capacitor using the ‘Show Power Consumed’ and ‘Show Average’ on the capacitors scope.

   • P_R^AVERAGE (mW) - Measure the average power consumed by the resistor using the ‘Show Power Consumed’ and ‘Show Average’ on the resistors scope.

   • P_V1 (mW) - Calculate the circuits real power consumption by using the supply voltage, supply current and phase measurement.

   • Q_V1 (mVAR) - Calculate the circuits reactive power consumption by using the supply voltage, supply current and phase measurement.

   • S_V1 (mVA) - Calculate the circuits apparent power consumption by using the supply voltage, supply current and phase measurement.

   • PF (-) - Calculate the circuits Power Factor.

2.4 Cleanup

Congratulations, you have completed the experimental part of the the laboratory. Before finishing, I’d suggest going through your results to check that you have completed everything and that your results make sense. If you find any issues, I’d suggest resolving or making a note of it now.

3 Results

The following is what you are expected to complete and submit for grading for Lab 4 before the deadline.

1. The completed Lab 4 - Results sheet template provided at the beginning of this lab manual under Equipment required. This sheet should include the following:

   • Your name, student ID and CCID.
   • All of the required measurements from the lab procedures.
   • All of the required calculations as discussed below.
   • The required plots as discussed below.

The Lab 4 - Results sheet needs to be submitted to the Submit (Lab 4 - Results) link on eClass as a pdf document .

2. Complete the online Quiz (Lab 4 - Post Lab) on eClass.

3.1 Plots

To create your plots you can use whichever software you would like (Paint, Excel, Matlab, etc) or simply draw them by hand if you like, but make sure it is tidy (you will need to scan and include it as an image in your report). Include your plot as an image and import it into your Lab 4 - Results sheet in the appropriate place.

Your plots should include:

• A Plot title
• Label your axes and show what unit of measure is used.
• For your phasor plots make sure to label the voltage, current and angle with their appropriate name and magnitude.

1. Individual Components - Phasor Diagram - Create a phasor diagram for the voltage and current for each individual component that you measured in section 2.1. (3 total). Don’t worry about the scales of the phasors just make sure to label the voltage, current and angle with their magnitudes.

2. Series RLC Circuit - Phasor Diagram - Create a phasor diagram for the series RLC circuit that you measured in section 2.2. Include the following signals: V_R(ref), V_S, V_L, V_C and I_S. Use V_R as you reference signal (0°). You need to make 1 phasor diagram for each frequency (4 total).

3. Series RLC Circuit - Power Triangle - Create a power triangle plot for the series RLC circuit that you measured in section 2.2. Include the following signals: P, Q and S. You need to make 1 power triangle plot for each frequency (4 total).

4. Parallel RC Circuit - Phasor Diagram - Create a phasor diagram for the parallel RC circuit that you measured in section 2.3. Include the following signals: V_S(ref), I_S, I_R, and I_C. Use V_S as you reference signal (0°). You need to make 1 phasor diagram for each frequency (3 total).

5. Parallel RC Circuit - Power Triangle - Create a power triangle plot for the parallel RC circuit that you measured in section 2.3. Include the following signals: P, Q and S. You need to make 1 power triangle plot for each frequency (3 total).

3.2 Questions

Complete the online Quiz (Lab 4 - Post Lab) on eClass.