Chapter 8
AC Power

m8.3 Complex Power

The circuit shown in Figure m8.3 operates in sinusoidal steady state at 1000 Hz. The voltage source amplitude is 2.5 V. Component values are: R = 100 Ω, C = 1.0 μF, and L = 3.3 mH.

1. Find the complex power in rectangular format for each of the four circuit elements: S_SRC, S_R, S_L, and S_C.
2. Demonstrate conservation of complex power with these four values.

NI Multisim Measurements

Enter the circuit of Figure m8.3 with an AC_VOLTAGE source. Set the “AC Analysis Magnitude” parameter to match the amplitude specified in the problem statement.

1. Run a Simulate → Analyses → Single Frequency AC Analysis to determine the complex powers S_SRC, S_R, S_L, and S_C in rectangular format.
2. Demonstrate conservation of complex power with these four values.

Additional helpful tips:

• The single-frequency AC analysis calls element power “P” (which suggests average power only) but in fact calculates complex power “S.”

NI myDAQ Measurements

Build the circuit of Figure m8.3. Activate the circuit with the NI ELVISmx Function Generator on AO0, and place an op amp voltage follower between AO0 and the remaining circuit; the voltage follower is necessary to boost the current drive of the analog output beyond its limit of 2 mA.

Use the NI ELVISmx Oscilloscope to display the device voltage on AI0. Display the voltage across resistor R on AI1, and realize that this voltage is proportional to the current through every device in the circuit.

1. Measure the complex power for each of the four circuit elements using the following procedure:
   • Read the RMS voltage V _rms from the oscilloscope numerical display,
   • Read the RMS current I_rms from the oscilloscope numerical display (divide the measured voltage by the resistance R),
   • Measure the time shift between the voltage and current sinusoids with the oscilloscope cursors,
   • Convert time shift to phase angle ϕ_Z = ϕ_v -ϕ_i (see Appendix F for details),
   • Note whether the current waveform lags or leads the voltage; ϕ_Z is positive when current lags and negative when current leads,
   • Express complex power as S = V _rmsI_rmsϕ_Z, and
   • Convert S to rectangular form.
2. Demonstrate conservation of complex power with these four values.

Additional helpful tips:

• Observe passive sign convention for each circuit element when measuring voltage and current: positive current enters the positive polarity terminal.
• Refer to Figure F.1 in Appendix F to learn how to measure amplitude and phase of a sinusoidal waveform.