- 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.
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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 / 2C = ____________; XL = 2L= ______________
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
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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?
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DC / AC Introduction Q3 2007
- Laboratory Experiments (Lab 9)
Series Resonance
1. Monitor the waveform across Vs and VR while adjusting the frequency until at resonance.
Remember that at resonance, XC = XL and the voltage across the resistor is a maximum because
maximum current flows at this time. Compare the measured resonant frequency to the calculated.
fr= ___________ measured
fr 
fr= ___________ calculated
1
2 LC
2. While adjusting the frequency measure the inductor voltage with the voltmeter. Monitor Vs with
the oscilloscope to maintain 5Vpp. Enter the data in Table 11-2 below.
Table 11-2
Frequency
VR
VC
VL
Frequency
1 kHz
6 kHz
2 kHz
7 kHz
3 kHz
8 khz
4 kHz
9 kHz
5 kHz
10 kHz
VR
VC
VL
3. Plot the frequency response of the resistor, capacitor and inductor voltages (with Excel).
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