ELEN 3441 – Fundamentals of Power Engineering Lab # 3 Spring 2008 Lab 3: Impedance.
Objective: to learn Ohm’s law for AC circuits; to solve complex AC circuits by the use of
impedance equation
Equipment: Power Supply, DAI, Variable resistance (8311), Variable capacitance (8331),
Variable inductance (8321)
Theory:
The impedance of serial connection of elements can be computed as:
Z = R2 + ( X L − X C ) ,
2
which indicates that, if the reactances are equal, the impedance is simply a circuit resistance with
a phase angle of zero.
The magnitude of the impedance of parallel connection of elements can be computed as:
Z=
or
Z=
RX C
R 2 + X C2
RX L
R 2 + X L2
When a circuit contains both inductive and capacitive elements, first solve for the total combined
reactance and then use its magnitude in the above expressions for the impedance. For series
circuits:
X = X L − XC
For parallel circuits:
X=
X L XC
X L − XC
The phase angle can be found from
cos θ =
A voltage drop across a resistor is:
R
Z
ER = I R R
Page | 1 ELEN 3441 – Fundamentals of Power Engineering Lab # 3 A voltage drop across an inductor is:
EL = I L X L
A voltage drop across a capacitor is:
EC = I C X C
Spring 2008 Experiment:
1) Using the Variable resistance and the Variable capacitance modules,
Figure 03-1.
Construct the following circuit as indicated in Figure 03-2:
Figure 03-2.
Include an additional voltmeter (E1) to measure the input AC voltage.
Set a resistance of the load to 150 Ω (use two 300 Ω resistors wired in parallel) and the
reactance to 100 Ω (use three capacitors with reactance of 300 Ω wired in parallel).
Page | 2 ELEN 3441 – Fundamentals of Power Engineering Lab # 3 Spring 2008 In the Metering window, open the Meter Settings dialog; select meter “A”, assign a meter
type “Phase shift” between E1 and I1 (input voltage and the circuit current), and apply
changes.
Figure 03-3.
Apply an input AC voltage of approximately 30 V and record the current through the
circuit, input voltage, voltage drops across the circuit elements, and the phase shift
between the input voltage and the circuit current.
Start the Phasor analyzer.
Figure 03-4.
Page | 3 ELEN 3441 – Fundamentals of Power Engineering Lab # 3 Spring 2008 Observe a phase shift between E1 and I1 (input voltage and the circuit current).
2) Replace the capacitive load by the inductive load using the Variable inductance module.
Figure 03-5.
The circuit will correspond to the diagram in Figure 03-6:
Figure 03-6.
Include an additional voltmeter (E1) to measure the input AC voltage.
Set a resistance of the load to 150 Ω (use two 300 Ω resistors wired in parallel) and the
reactance to 100 Ω (use three inductances with reactance of 300 Ω wired in parallel).
Page | 4 ELEN 3441 – Fundamentals of Power Engineering Lab # 3 Spring 2008 Apply an input AC voltage of approximately 30 V and record the current through the
circuit, input voltage, voltage drops across the circuit elements, and the phase shift
between the input voltage and the circuit current.
3) Using the Variable resistance, Variable capacitance, and Variable inductance modules,
construct the circuit shown in Figure 03-7:
Figure 03-7.
First, connect one of the voltmeters (E1) to control the input voltage. Set the load
resistance R to 100 Ω, and the reactances XC = 150 Ω, XL = 300 Ω. Apply an input
voltage Es of approximately 30 V. Observe and record the exact values of input voltage,
circuit current and the phase shift between Es an I.
Next, without turning the PS OFF and readjusting the input voltage, reconstruct the
circuit Figure 03-7 by connecting the voltmeter E1 back to its original position. Note: use
extra caution when making any connections while the power in the circuit is ON even
though the circuit voltages are relatively low!
Record the current through the circuit and the voltage drops across the circuit elements.
Observe that the circuit current must be (almost) exactly equal to the value you recorded
previously. Also note that voltage across one of the reactive elements may be higher than
the input voltage!
4) Construct the circuit shown in Figure 03-8.
Page | 5 ELEN 3441 – Fundamentals of Power Engineering Lab # 3 Spring 2008 Figure 03-8.
Note: since only three ammeters are available, first replace one of the load ammeters by a
wire and use this ammeter to measure the current through the circuit. Also, connect the
E1 voltmeter to measure the input voltage.
Set the load resistance to 100 Ω and both load reactances to 300 Ω. Apply an input AC
voltage of approximately 30 V and record the values of input voltage, circuit current and
phase shift between them.
Turn the power OFF without touching the voltage adjustment knob. Modify your circuit
such that all three ammeters will measure load currents. Turn ON the PS and record the
values of currents through the resistive, capacitive, and inductive loads.
Turn OFF the PS and disassemble your circuit.
In your report:
1. For the values of resistance and reactance used in Part 1, calculate the load impedance
and the phase angle between the input voltage Es and the circuit current. For the
measured input voltage and the calculated impedance, evaluate the circuit current. Is the
calculated value of circuit current approximately equal to its measured value? Using the
calculated circuit current, calculate the voltages across the resistor and the capacitor. Are
these values approximately equal to the values measured in Part 1? Discuss possible
sources of discrepancy.
2. For the values of resistance and reactance used in Part 2, calculate the load impedance
and the phase angle between the input voltage Es and the circuit current. For the
measured input voltage and the calculated impedance, evaluate the circuit current. Is the
calculated value of circuit current approximately equal to its measured value? Using the
calculated circuit current, calculate the voltages across the resistor and the capacitor. Are
these values approximately equal to the values measured in Part 2? Discuss possible
sources of discrepancy.
3. For the values of resistance and reactances used in Part 3, calculate the load impedance
and the phase angle between the input voltage Es and the circuit current. For the
Page | 6 ELEN 3441 – Fundamentals of Power Engineering Lab # 3 Spring 2008 measured input voltage and the calculated impedance, evaluate the circuit current. Is the
calculated value of circuit current approximately equal to its measured value? Using the
calculated circuit current, calculate the voltages across the resistor, the inductor, and the
capacitor. Are these values approximately equal to the values measured in Part 3?
Discuss possible sources of discrepancy. Assuming that reactances of inductive and
capacitive loads are both equal to 150 Ω, predict and report the value for the load
impedance.
4. For the values of resistance and reactances used in Part 4, calculate the load impedance
and the phase angle between the input voltage Es and the circuit current. Are the
calculated and measured values of the phase shift approximately equal? Using the
measured input voltage and the values of resistance and reactances set for the loads,
calculate the currents through each load. Do the measured values of load currents
approximate their calculated values? Calculate the total current flowing through the
circuit and compare it to the value you measured in Part 4. Are they approximately equal?
Discuss possible sources of discrepancy.
Page | 7