Chapter 8
AC Power

m8.2 Average Power

The circuit shown in Figure m8.2 operates in sinusoidal steady state at 1500 Hz. The voltage source amplitude is 3 V. Find the average power delivered by the source. Use these component values: R = 100 Ω, C = 1.0 μF, and L = 3.3 mH.

NI Multisim Measurements

Enter the circuit of Figure m8.2 with an AC_VOLTAGE source, setting its peak value and frequency according to the values specified in the problem statement. Place a Simulate → Instruments → Wattmeter instrument to measure the voltage source power. The wattmeter displays average power in sinusoidal steady state.

NI myDAQ Measurements

Build the circuit of Figure m8.2. 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 voltage source on AI0; this voltage serves as the reference sinusoid for phase measurement. Display the voltage across the resistor on AI1, and realize that this voltage is proportional to the voltage source current.

Calculate average power from three measurements: voltage source magnitude, current magnitude, and the phase difference between the source voltage and current.

Additional helpful tips:

• The oscilloscope numerical display shows the RMS voltage of the waveforms. Use the appropriate equation for average power based on these RMS voltages.
• The oscilloscope numerical display also shows the peak-to-peak voltage of the waveforms. One half of this value is the amplitude of a sinusoidal waveform. If you choose this measurement, use the appropriate equation for average power based on amplitudes.
• Refer to Figure F.1 in Appendix F to learn how to measure amplitude and phase of a sinusoidal waveform.

Further Exploration with NI myDAQ

The power delivered by the voltage source depends on it frequency:

1. Monitor the voltage source current on the oscilloscope and adjust the voltage source frequency to maximize the current amplitude, thereby maximizing the average source power delivered to the circuit. Record the voltage source frequency f_max at which the source average power is maximized, and then calculate the average power delivered by the source at this frequency.
2. Calculate the impedance of the inductor and capacitor at f_max. Explain how these impedance values relate to maximizing the average power delivered by the source.
3. Adjust the voltage source frequency in a range above and below f_max and observe the phase difference between the source voltage and current. Discuss your observations.