- Laboratory Experiments (Lab 9) DC / AC Introduction Q3 2007 BACKGROUND: True Power and Apparent Power 18. In AC circuits, the power dissipated in a resistor is referred to as true power (P). In an AC circuit containing inductors and capacitors, we also have what we refer to as apparent power (S). This is a combination of the true power plus reactive power (Q). Reactive power is the energy stored in the electric field of the capacitor, or in the magnetic field of the inductor, during one half cycle of the input waveform, and returned to the source during the second half cycle when the source voltage reverses polarity. 19. The rate at which such energy is stored and returned to the source is measured not in Watts but in Volt-Amperes-Reactive, or VARs. Reactive power (Q) is calculated by one of the following formulas: a) b) c) 20. Preact = I2XC or I2XL Preact = VS I sin Preact = VC2 /XC or VL2 /XL The apparent power (S) in an AC circuit is the total power that the circuit appears to be dissipating. It’s units are Volt-Amperes (VA). Apparent power is found by the phasor sum of Real Power and Reactive Power. Papp = Ptrue 2 Preact 2 . It may also be determined by using one of : a) b) c) 21. 22. Papp = I2Z Papp = VS I Papp = VS2 /Z The Power Factor ( pf ) of a circuit is a measure of how large the reactive component of the Apparent Power is. If a phasor diagram or “power triangle” showing True and Apparent Power is constructed, then the Power Factor is the cosine of the angle between these two phasors. Ptrue Power factor is found from cos = P / P true app Preact Papp In industrial applications, a pf close to 1.0 ( = 0) is desirable. Techniques such as the addition of XC in order to balance out the XL and minimize Preact are used to achieve this. Equipment such as capacitor banks and over excited synchronous machines are typically used to correct a poor power factor. A pf of 0.90 to 0.95 is usually considered minimum and a financial penalty is typically paid by a company whose power factor dips below this amount. Penalties are also assigned for too much peak demand, especially during the daytime. ELEX 247 Lab 10 revised 2008 Page 1 of 4 DC / AC Introduction Q3 2007 - Laboratory Experiments (Lab 9) PROCEDURE - True and Apparent Power in a Series RLC Circuit 23. Set up the circuit of Figure 9-2 as shown below: Figure 9-2 R1 L1 1 kΩ 100 mH Vs 4 Vrms 6 kHz C1 0.01 F 24. Adjust the signal generator to produce a 6 kHz sine wave and verify that you measure 4.0 Vrms across the circuit. 25. Calculate XC and XL. XC = 1 / 2C = ____________; XL = 2L= ______________ 26. Draw the impedance diagram for Figure 9-2. Include the resultant circuit impedance Z. 27. Calculate the power factor : PF = cos 28. Calculate: I rms = VS rms / Z 29. Using the results of steps 4 and 5 calculate: (a) Ptrue = VS * I cos (b) Preact = VS * I sin (c) Papp = VS * I ELEX 247 Lab 10 revised 2008 Page 2 of 4 DC / AC Introduction Q3 2007 - Laboratory Experiments (Lab 9) 30. Sketch and label the phasor diagram of the theoretical circuit power (power triangle). 31. Using an voltmeter, measure the voltages VR, VL, and VC . VR = ____________ VRMS VL = ____________VRMS VC = ____________VRMS 32. Draw the phasor diagram of the circuit voltages. VS ,VR and the resultant of the reactance phasors, (VL -VC). This is a labelled sketch and does not have to be to scale. 33. Calculate: (a) Ptrue = VR2 / R = ___________ milli-Watts (b) Preact = (VC – VL)2 / (XC – XL) = ___________ milli-Volt-Amps Reactive 34. Sketch the phasor diagram of the measured circuit power. 35. Does the phasor from step 30 agree with the phasor of step 34? Why or why not? ELEX 247 Lab 10 revised 2008 Page 3 of 4 DC / AC Introduction Q3 2007 - Laboratory Experiments (Lab 9) fr 1 2 LC Table 11-2 ELEX 247 Lab 10 revised 2008 Page 4 of 4