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University of Sharjah
Electrical and Electronics Engineering Department
0402203
Circuit Analysis I Laboratory
Experiment # 11
Phasor Domain Measurements for AC Circuits
Objective:
1. To experimentally verify frequency domain calculations using phasor method.
2. Experimentally measure the phase difference between two sinusoidal signals.
3. Calculation of Average Power from the measured quantities.
Pre-Lab Assignment:
For the circuits shown in Figure 1:
1. Assume that the inductor has internal resistance of 36 ohms.
2. Let the source voltage Vs has peak-to-peak amplitude of 10 V and frequency of 20kHz.
Assume that Vs has zero phase shift.
3. Use phasors method to calculate all voltages and currents shown.
4. Verify your results using PSpice.
Enter your results in Tables 2 and 3
Figure1
Apparatus:
 Signal Generator
 Digital Multimeter
 Oscilloscope
 Capacitor 0,022 F
 Inductor 10mH
 Resistors: 10 , 1 k, 1.5 k.
Theory:
In the frequency domain (phasor domain), the currents and voltages are represented by complex numbers
whose magnitudes are equal to the maximum values of the sinusoidal time- domain quantities, and whose
angles are equal to the phase angles of the time-domain functions expressed as cosines. In terms of voltage
and current phasors and the complex impedance Z, Ohm's law becomes:
V= Z I
where Z= R for a resistance
= j  L for an inductor
1
=
for a capacitance
j C
where  = 2 f is the angular frequency of the source. The bar indicates a complex quantity.
V
In general, for V = V and I = I , the impedance Z = -
I
Analytically, frequency-domain circuits are treated by the same method as used in DC circuits, except that
the algebra of complex numbers is used. Experimentally, the frequency-domain phasors can be measured
on the oscilloscope. The magnitudes can be measured by means of calibrated vertical scales. Phase
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difference can be measured by using the dual traces and measuring the time difference between two
waveforms, as illustrated in Figure 2.
Average power For sinusoidal sources average or real power can be expressed as
Pavg 
1
Vm I m cos(   )
2
(for sinusoidal)
Where θ-φ : is the phase angle difference between v(t) and i(t)
The average power for the three passive elements will be:
For R: The phase shift is 0  Pavg
1
Vm2
1
 Vm I m 
 I m2 .R
2
2R
2
For L & C: The phase shift is 900  Pavg = 0
This means that L and C do not dissipate power. They just store it for later use. The average power is zero
for reactive elements but the instantaneous power is not zero all the time.
IMPOTANT NOTE: When measuring the phase difference between two signals: make sure that the
control knobs in the oscilloscope are set properly such that the signals are not relatively inverted.
Procedure:
1- Measure the resistor values and the internal resistance of the inductor, using an Ohmmeter and record
your results in Table.1
2- Connect the circuit of Figure 1. Adjust the source voltage to 10 V peak-to-peak at 20 kHz, while it is
connected to the circuit.
3- Use the oscilloscope to measure the magnitudes and phases of V1 V2 V3 and V4 with reference to the
source voltage.
4- Find I1 .and I3 from V1 and V3. Find I2, from the measurement of voltage across the 10  resistor in
series with the capacitor.
IMPORTANT NOTE: Whenever two signals are to be displayed simultaneously on the oscilloscope, they
should have one common node as a reference. Therefore, you may have to change the position of some
elements to be able to measure two signals simultaneously.
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Report:
1- Draw the circuit of Figure 1 in the frequency domain (in the phasor representation).
2- Record the theoretical and experimental values in Table 2.
3- Write down the time functions (instantaneous representation) for the voltages and currents in Table 3.
4- Draw the phasor diagram, showing all the voltages and currents, based on the experimental values.
5- Discuss the sources of discrepancies between the theoretical and experimental values.
Questions:
1- For a. resistance and a capacitance in series with a voltage source, show that it is possible to draw a
phasor diagram for the current and all voltages from magnitude measurement of these quantities only
illustrate your answer graphically.
2- The equivalent impedance of a capacitor in series with an inductor is equivalent to a short circuit (i.e.
Zeq = 0) at a certain frequency. Derive an expression for this frequency in terms of C and L.
3- The equivalent impedance of a capacitor in parallel with an inductor is equivalent to an open circuit
(Le. Zeq =) at a certain frequency. Derive an expression for this frequency.
4- Calculate the average (real) power supplied by the source. Also calculate the average power absorbed
by all the circuit elements in Fig. 1.
Table 1
Resistor
Nominal Value (ohm)
Ohmmeter Reading
R1
10 
R2
1 k
R3
1.5 k.
Internal resistance of the inductor =
Table 2: Voltage and Current Phasors (Circuit of Figure 1):
Theoretical
V1
Calculated
Values
PSpice
Values
Experimental
Values
V2
V3
V4
I1
I2
I3
Magnitude
Phase
Magnitude
Phase
Magnitude
Phase
Magnitude
% Error
Phase
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Table 3: Time Function of Theoretical and Experimental Voltages and Currents:
Theoretical
Experimental
v1(t)
v2(t)
v3(t)
v4(t)
i1(t)
i2(t)
i3(t)
Circuit in Frequency domain
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Phasor Diagram
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