ENGI 241 EXPERIMENT 8
AC MEASUREMENTS I
PURPOSE
At the conclusion of this experiment, the student will be able to determine the capacitive and inductive
reactances, the net circuit reactance, the impedance, plus current and voltage drops in the series RLC
circuit.
EQUIPMENT AND MATERIALS REQUIRED
2 each DMM'S
Oscilloscope
Powered Protoboard
Audio Signal Generator
Frequency Counter
Resistors, 1/4W, 5%, 910Ω.
Inductor, 10%, 90Ω winding resistance, 62mH
Capacitor, Tantalum, 35V, 10%, 0.15µF
INTRODUCTION
At different frequencies, for a sinusoidal input, the capacitive reactance and the inductive reactance
change. However, as the frequency increases, XC decreases while XL increases. Since XC and XL are
antiphase (180° out of phase), one reactance tends to cancel the other. In the series RLC circuit of
Figure 8 − 3, the total impedance in the circuit is the phasor sum of all the resistances and reactances
of the circuit. The total impedance of the circuit can be found from the equation:
ZT = R + ( JXL − jXC )
Let's define the net reactance of the circuit as XX, which is the phasor sum of XC and XL. XX will be
capacitive if XC is greater than XL, and the circuit characteristics will be that of the RC circuit. When
XC is less than XL, XX is inductive, and the circuit will have RL circuit characteristics.
As a result, the series RLC circuit behaves like an RC circuit at frequencies below the resonant
frequency, since XC is large and XL is small. At frequencies above the resonant frequency, the
frequency where XC is less than XL, the series RLC circuit behaves like an RL circuit since XL is larger
than XC. Therefore, equation <8 − 1> may be written as:
ZT = R ± j XX
The impedance phasor diagram for the series RLC circuit at some frequency
below resonance, is shown in Figure 8 − 1. For Figure 8 − 1, assume the
total circuit resistance is 700Ω, Xc is − j 1200Ω, and XL is +j 600Ω. The net
reactance and net impedance are:
XX = − j 1200Ω + j 600Ω = − j 600Ω
∴ ZT/ θ = 700Ω − j600Ω
FIGURE 8 − 1
ZT = 922Ω /−40.6o
For the same circuit, if XL is + j 1200Ω and XC is − j 600 the circuit would be operating above
resonance, since the inductive reactance is larger than the capacitive reactance. Of course, the total
circuit resistance would remain the same. The impedance phasor diagram for the circuit would now
look like the one shown in Figure 8 − 2. The phase angle is positive and the circuit behaves like an RL
circuit. The calculation for the total circuit impedance is:
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ENGI 241 EXPERIMENT 8
AC MEASUREMENTS I
ZT = R + ( j XL − j XC ) = 700Ω + j1200Ω − j 600Ω = 922Ω/40.6o
Since the series circuit forms a voltage divider, there will be voltage drops
across each component. Therefore, the voltage phasor diagram will look
exactly the same as the phasor diagram shown in Figure 8 − 2, when the
circuit is operating above the resonant frequency and like Figure 8 − 1 when
operating below the resonant frequency. However the phasors will be
labeled VL instead of XL, VC instead of XC and VRT instead of RT. The
resultant phasor will be VS instead of ZT.
FIGURE 8 − 2
NOTE
In the above examples, the dc winding resistance of the inductor was not considered when
solving for the circuit parameters, or in illustrating the phasor diagrams. During the
performance of this experiment, the student should include the winding resistance of the
inductor in all calculations and phasor diagrams.
PROCEDURE
1. Measure and record the component values. Be sure to include RL1, the
winding resistance of the inductor as a series resistance with XL
2. For Figure 8 − 3, assume R1 is 910Ω, C1 is 0.15µF, L1 is 62mH, and
VS is 5 Vrms at a frequency of 500 Hz. Determine and record the
calculated values for Table 8 − 1.
3. Build the circuit of Figure 8 − 3, with the component values stated in
step 1. Adjust the supply voltage to 5Vrms at a frequency of 500Hz.
Measure the voltage drops and phase angles, and record the data in
Table 8 − 2. Measure the total circuit current and its phase angle.
Record this data in Table 8 − 1 as measured values.
FIGURE 8 − 3
4. Using the measured data from step 2, calculate the capacitive
reactance, the inductive reactance, and the total circuit impedance. Record this data as measured
values in Table 8 − 1.
5. From the total impedance, obtained in step 3, determine the net reactance and record this data as
the measured value in Table 8 −1.
6. Repeat steps 1 through 4 when using a 3kHz source frequency.
7. Run a PSpice transient analysis for the circuit in Figure 8 − 1 at 500Hz and 3kHz. Use the supply
voltage as the reference. Create separate plots for each voltage drop vs. vs for two to three cycles.
Compare to the magnitudes and phase shifts to the measured data.
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ENGI 241 EXPERIMENT 8
AC MEASUREMENTS I
Component
R1
C1
L1
RL1
Rated Value
910Ω
0.15µF
62mH
90Ω
Measured Value
Note: RL1 = Inductor Winding Resistance
Frequency
500 Hz
XL
XC
ZT∠θ
XX
IT∠θ
Calculated
Measured
Calculated
3 kHz
Measured
TABLE 8 - 1
VC
500 Hz
VL
Calculated
Measured
3 kHz
Calculated
Measured
TABLE 8 - 2
Page 3
VX
VS∠θ