FVCC Engineering Laboratory
Inductive Reactance
Using NI ELVIS
J.K. Boger∗
March 28, 2012
∗
jboger@fvcc.edu
1
FVCC EELE 101
1
AC inductive reactance
2
Objective
In this lab we will explore how inductors react in circuits driven by AC voltage sources. Specifically we
will gain experience with:
1
2
3
4
2
Inductive reactance
Impedance in an RL circuit driven by an AC source
The National Instruments ELVIS platform
Packaged Virtual instruments for the ELVIS board.
Equipment
The basic equipment for this experiment is as follows:
1
2
3
4
5
6
7
8
3
Resistor of about 2000[Ω]
Inductor of about 10 − 25[mH]
NI ELVIS workstation
Computer with LabVIEW installed
Jumper wire set
Multimeter for measuring resistance
LRC meter for measuring capacitors
Excel for recording and processing data
Theory
This lab is the second in a series of AC labs and will concentrate on the behavoir of the inductor. The
inductor and the capacitor behave in similar fashion when part of an AC driven circuit. The biggest
difference is that they are completely out-of-phase with one another. The reason for this is rooted in
what they do from a physics perspective. Capacitors ’store’ charge. More accurately, capacitors store
separated charge that produces an electric field between them. Consequently, it is more accurate to say
that a capacitor stores energy in the form of an electric field. Since it takes time to build up, or remove
this energy, capacitors have unique responses to AC sources. Inductor also store energy. The difference
is that the energy is in the form of a magnetic field. Since magnetic fields are produced by current, it
takes a current to build stored energy in an inductor. Furthermore, it takes time to build up this stored
energy just as in the capacitor. So, inductors behave very similar to capacitors, and much of the theory
we studied in the previous lab also holds true for this lab.
FVCC EELE 101
AC inductive reactance
3
Most importantly, the vector concepts introduced for the previous lab also hold for this lab. We
will be interested in inductive reactance, impedance, and phase angles and vectors are a mathematical
tool which greatly aid the analysis. This lab is about further practice using the basic tools for series AC
circuits.
3.1
Inductive Reactance
When an RL circuit is driven by a sine wave (AC signal) the response or voltage drop on the inductor is also a sine wave of the exact same frequency. This is precisely what happened in the case of
an RC circuit. Inductors are simply coils of wire so they pass DC current without much more resistance than that which is inherent to the wire. But when the current is changing, the inductor resists the
change. This resistance is then what constitutes the inductive reactance and is quantified by equation 1.
Inductive reactance is the AC resistance to the current in an inductor. It is directly
proportional to circuit frequency and it is measured in Ohms [Ω].
XL = 2πf L
(1)
In this equation, L is the symbol for inductance. It is measured in units of henries [H]. The fundamental
. Inductive reactance is used in a circuit just like resistance in Ohm’s law
units of the henry are H = v·s
A
as long as we use peak voltage and peak current rather than the time varying terms in the AC signal.
Here Vp ,Ip refer to the peak values.
Vp = Ip Xc
(2)
When Inductors are put in series with resistors, the inductive reactance combines with resistance to form
impedance, Z. Impedance is the collective resistance to the AC circuit. Impedance for a series circuit is
given by equation 3.
p
(3)
Z = Xc2 + R2
As there was with capacitors, so also is there an important relationship between the phases of the
instantaneous voltage and current in inductors that arises due to an inductor’s reaction to changing
currents. In an inductor, the instantaneous current ’through’ the inductor lags the instantaneous voltage
across the inductor by 90 degrees. That is, IL lags VL by 90o . Since the instantaneous current through
all series circuit components must be in phase, and the since the current through and the voltage across
the resistor are in phase, then the inductor’s voltage leads the resistor’s voltage by 90o . This is diagramed
in Figure 1. You should compare this diagram with the vector diagram in the capacitive reactance lab.
The vector diagram can be used to find voltages in an AC circuit as well as phases. As can be seen,
FVCC EELE 101
AC inductive reactance
4
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Figure 1: Voltage phase illustrated by a phasor diagram.
equation 3 is simple the pythagrean theorem applied to Figure 1. Likewise, phase is easily determined
from the figure. The phase between the resistor and the source voltage is given by equation 4 and the
phase between the inductor and the source voltage is given by equation 5.
R
φr = atan
(4)
XL
XL
(5)
φL = atan
R
Because our series circuit is basically a voltage divider, it is no surprise that the voltage expected across
each component will follow the voltage divider equation.
Vs R
Vr =
(6)
Z
Vs XL
VL =
(7)
Z
4
Procedure
The goal is to build a series RL circuit and measure the AC voltage response in term of amplitude and
phase for both the resistor and the Inductor. Since reactance is a function of input frequency, we will
collect data from 10 [Hz] to 50 [kHz] as outlined in the data tables. We will then calculate the expected
FVCC EELE 101
AC inductive reactance
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Figure 2: Circuits needed.
voltage and phase responses. The tables will be completed in Excel and the data plotted from there.
The circuits needed are shown in Figure 2. Note that your resistance and Inductance values will not be
the same as shown in these circuits.
4.1
Experiment Set-Up
1. Select a Inductor and resistor close to the values given in the equipment list. Measure their exact
values with the appropriate meter. Save these values.
2. On the National Instruments ELVIS board, build a series RL circuit.
3. Wire the positive probe on the scope from AI 0 to the junction between capacitor and resistor. If
the capacitor is connected to ground, than AI 0 will measure the voltage across the inductor.
4. Wire the positive probe on the scope from AI 1 to the output of the function generator. This will
read the source voltage.
5. Open National Instruments ELVIS instrument launcher. You may need to search for this in the
program start-up.
6. Power on the EVLIS unit. There are two power switches on the upper right and both need to be
on.
7. From the instrument launcher, open the oscilloscope and the function generator.
FVCC EELE 101
AC inductive reactance
6
8. Be sure the Device is set to ”Dev1 (NI ELVIS II+)”. This should happen automatically at start-up.
If it is not there, check to see that power is on and cables are connected. Close the program and
relaunch to fix this. It may actually say ”Dev2 (NI ELVIS II+)” or similar which will work.
9. Set the scope to read AI 0 for the first channel and AI 1 for the second channel. You will have to
check the enable box on channel 2 to activate it.
10. Set the function generator on Vp−p = 1.0[V ] and f = 100[Hz], sine wave output.
11. Set the trigger on the oscilloscope to normal
12. Run the function generator, then run the oscilloscope.
4.2
Measured Data: Table 1
13. Open Excel and build the data table shown in Table 1
14. Collect data for the inductor at each frequency setting. The data will be the peak source voltage,
the peak inductor voltage and the phase between the two. Note that phase will be measured in
µs. The next column in Table 1 is the phase converted to degrees. The formula for converting
from µs to deg is:
360 · f · ∆t
(8)
φ=
1000
15. After collecting all the data on the inductor, reverse the direction of the signal by wiring the function
generator to the inductor first and grounding the resistor side of the circuit. Now, without moving
the AI 0 signal, we have changed from measuring inductor voltage to measuring resistor voltage.
16. Fill out the same data for the resistor as you did for the inductor. This will complete the actual
data taken from the real circuit.
17. Calculate the total phase by summing the measured phase of the resistor and the inductor. It
should be 90o .
18. Calculate inductive reactance for each resistance using equation 1.
19. Resistance is simply repeating the value of resistance you made at the start.
20. Calculate impedance using 3.
21. Calculate the expected inductor value using the voltage divider expression for inductance.
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22. The last column in this table is the sum of the resistor-source phase and the inductor-source phase.
It should be 90o . The amount that is differs from 90o is a measure of the noise in your circuit. If
it is more than 15o from the expected value, go back and check your data.
4.3
Calculated data: Table 2
23. Build Table 2 in Excel.
24. Fill each column of Table 2 using the formulas in section 3. The ’Resistor’ column is simply the
value of resistance measured at the start of the experiment.
4.4
Data Analysis
25. Create plots of the data. Plot the inductor voltage verses frequency. Plot the Calculated values
from Table 2 as a solid line. Then on the same chart, plot the experimental values from Table 1
as points without a connecting line. An example of this plot is shown in Figure 3.
26. Plot the resistor voltage verses frequency in the same fashion you plotted the inductor data.
27. Plot the inductor phase verses frequency together with the resistor verses phase and the sum of
the two phases. Plot the calculated and measured data in the same fashion as the voltage data.
Your plot should have 3 curves on it with measured data plotted as points.
Revision date: March 28, 2012
FVCC EELE 101
AC inductive reactance
Table 1: Measured Data
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