Prelab 5

Recall that average power absorbed by a circuit element is V_rmsI_rmscos(θ-φ) where θ-φ is the phase difference between the element's sinusoidal voltage v(t) and current i(t). To obtain the most efficient use of the current delivered to a load, it is desired that the load voltage and current be in phase (θ-φ = 0, PF = 1) such that average power is maximized. The purpose of this lab is to add compensation to an inductive load such that its equivalent power factor becomes close to 1.

Notes on Measurements:

• Experimental determination of the power factor typically requires the measurement of the phase difference between voltage and current. Two properties of the function generator and oscilloscope make this measurement difficult.
  • The reference (ground) leads on the oscilloscope and function generator are internally tied to ground making it imperative that they all be connected to the same point in the circuit.
  • The difference between channels 1 and 2 (CH1-CH2) can only be displayed by itself on the oscilloscope.
• Carefully consider where to take measurements such that subject to the above constraints the information of interest can be determined.

Laboratory Procedure:

1. Investigate inductive load
• An inductor is a coil of wire and wire has resistance. Measure the resistance of your 0.47mH inductor. If this resistance is significant include it your calculations.
• Construct the following circuit.

• Experimentally determine the load impedance Z_L, power factor angle θ-φ, power factor PF, and complex power using voltage and current measurements. Compare these to your predicted values found in the prelab.
2. Load power factor correction
• Add a capacitor of the value determined in the prelab in parallel with the original load as shown in figure 2. Note the value of the capacitor may need to be updated based upon the resistance of the inductor.

• Verify that your power factor correction is working. Due to the measurement constraints described above, it might be easier to verify your power factor correction by comparing the load voltage to the source voltage. What should this relationship be and how does it compare to your experimental results?
• Normally, it isn't a good idea to change a circuit with input and power applied, but carefully insert and remove the capacitor while watching the source and load voltages to easily see the effect of the compensation.
• Does your load compensation work at other frequencies other than 10kHz? Investigate this both mathematically and experimentally. Is there a difference in the load as frequency is increased versus decreased?