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ACTION: Apply the theory of power circuits and transformers.
CONDITIONS: Given a LabVolt EMS system, LabVolt courseware,
Fluke electrical metering devices, and applicable references.
STANDARD: Effectively use transformers and power circuits theory to
solve complex engineering problems in an austere environment.
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• Safety Requirements: None
• Risk Assessment Level: Low
• Environmental Considerations: None
• Evaluation: Students will be evaluated on this
block of instruction during the Electrical Systems
Design Examination 1. Students must receive a
score of 80 percent or above to receive a GO.
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ACTION: Apply Fundamentals Inductors in AC Circuits.
CONDITIONS: Given a LabVolt EMS system, LabVolt courseware,
Fluke electrical metering devices, and applicable references.
STANDARD: Use circuit measurements to determine the inductive
reactance of inductors, and you will measure and observe the phase
shift between voltage and current caused by inductors.
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• When you have completed this unit, you will be able to
demonstrate and explain the effects of inductors in ac
circuits.
• You will use circuit measurements to determine the
inductive reactance of inductors, and you will measure and
observe the phase shift between voltage and current
caused by inductors.
S3D03-6
Lesson Objectives
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• The exercises in this unit are quite similar to those in Unit 3,
and as you will discover, inductor behavior in electric
circuits is the converse to capacitor behavior in electric
circuits.
• Both components store energy, and both cause a phase
shift of 90° between voltage and current.
• Capacitors store energy in an electric field set up by the
application of a voltage, while inductors store energy in a
magnetic field set up by a current that flows in a coil of
wire.
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• Inductors are frequently called chokes or coils. The entire
electrical industry revolves around coils, which are found in
motors, generators, relays, and numerous other electrical
devices.
• The fundamental property of inductors is to oppose
changes in the current flowing through its coil.
• The opposition to current changes is proportional to the
inductor's inductance (L).
• The inductance is a measure of the amount of energy that
an inductor stores in the magnetic field set up when a
current flows through its coil, and the measurement unit for
inductance is the henry (H).
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• When inductance is added to an ac circuit, an effect similar to
that of capacitance is observed, that is, there is opposition to the
flow of current.
• This effect is referred to as the inductive reactance (XL), which
is defined as the opposition created by inductance to the flow of
alternating current.
• When current flows through a coil of wire, a magnetic field is set
up and this field contains energy.
• As the current increases, the energy contained in the field also
increases.
• When the current decreases, energy contained in the field is
released, and the magnetic field eventually falls to zero when the
current is zero.
• The situation is analogous to the capacitor, except that in a
capacitor, it is the voltage that determines the amount of stored
energy, while in the inductor it is the current.
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• Consider the inductive circuit shown in Figure 4-1.
• The ac power source will cause alternating current flow in
the inductor coil, and the current will increase, decrease,
and change polarity in the same alternating manner as the
source voltage.
• Consequently, the coil will alternately receive energy from
the source and then return it, depending on whether the
current through the inductor is increasing (magnetic field is
expanding) or decreasing (magnetic field is collapsing).
• In ac circuits, power flows back and forth between the
inductor and the power source and nothing useful is
accomplished, just like the case for capacitors.
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• If a wattmeter were connected to measure the power
consumed by an ideal inductor, it would indicate zero.
• In practice however, all coils dissipate some active power
and the wattmeter indicates a small amount of power.
• This is because the coil wire always has resistance, and
therefore, dissipates power as a resistor does.
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• There is a voltage drop across the inductor and current
flows in the inductive ac circuit in a way very similar to the
purely capacitive circuit.
• The apparent power (E x I product) is equal to the reactive
power in the case of the ideal inductor, and the
instantaneous power waveform shows that there are
instances of both positive and negative power peaks like it
does for capacitive ac circuits.
• In order to distinguish between capacitive reactive power
and inductive reactive power, a negative sign is usually
associated with capacitive var, and a positive sign with
inductive var.
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• When you have completed this exercise, you will be able to
determine inductive reactance by using measurements of circuit
currents and voltages.
LSA 1: Inductive Reactance
Time: 4 hrs
PE: 50 mins
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• Inductive reactance is defined as the opposition to
alternating current flow caused by inductance.
• Inductance is a property of inductors and increases when
the inductor has an iron core.
• The measurement unit for inductance is the henry (H).
• Its effect is very similar to that caused by capacitance, and
like capacitive reactance, inductive reactance changes with
frequency.
• However, since it is directly proportional to frequency,
inductive reactance increases when the frequency
increases, which is opposite to capacitive reactance.
• Also, increasing an inductor's inductance increases its
inductive reactance.
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• When a dc voltage is applied to an inductor, a dc current flows
through the inductor's coil.
• Because the dc current does not change with time, the inductor
does not oppose current flow and the current magnitude is only
limited by the resistance of the coil wire.
• When an alternating voltage having an rms value equal to the dc
voltage is applied to the same inductor, an alternating current
flows through the inductor's coil.
• Because the current changes continuously, the inductor opposes
changes in current and the current magnitude is limited to a
much lower value than that obtained with the dc voltage.
• The greater the inductance of the inductor, the greater the
opposition to current changes.
• The opposition to ac current flow caused by an inductor is
referred to as inductive reactance.
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• The formula for determining inductive reactance in an ac
circuit is as follows:
• The formula for determining inductive reactance shows that
it is directly proportional to frequency and inductance,
and will double whenever the frequency or the inductance
is doubled.
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• familiar Ohm's law, which gives XL=EL/IL, along with the
equivalent expressions and IL=EL/XL and EL=IL x XL. EL and
IL used in these expressions represent rms voltage and
current values.
• These expressions of Ohm's law, along with the laws of
Kirchhoff seen in earlier exercises are all valid for solving
inductive ac circuits.
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• In this exercise, you determined the inductive reactance for
different ac circuits using Ohm's law and measurements of
circuit voltages and currents.
• You also observed that Ohm's law is valid for inductive ac
circuits, and demonstrated that reactance changed in direct
proportion to the amount of circuit inductance.
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• When you have completed this exercise, you will be able to determine the
equivalent inductance for series and parallel inductors.
• You will also be able to explain and demonstrate equivalent inductance using
circuit measurements of current and voltage.
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• Inductors are electrical devices made up of a coil of wire wound around a core.
• The core material can be non-magnetic like wood or plastic, or magnetic
material like iron or steel. Inductors made with non-magnetic cores are called
air-core inductors, while those with iron and steel are iron-core inductors.
• Using magnetic materials for the core allows greater values of inductance to be
obtained because magnetic materials concentrate the magnetic lines of force
into a smaller area.
• Figure 4-3 shows examples of air-core and iron-core inductors.
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• An inductor stores energy in the magnetic field created around its coil of wire
when the current through the coil changes.
• The amount of energy that the inductor can store depends on its inductance,
the type of core, and the number of turns of wire.
• The measurement unit for inductance, the henry (H), is the value obtained
when current changing at a rate of one ampere per second causes a voltage of
one volt to be induced in the inductor.
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• The formulas used to determine equivalent inductance are the same form as
• those used for equivalent resistance.
• As in the case for resistance, equivalent inductance LEQ is greater for series-
connected inductors, while it is smaller for parallel combinations.
• Series and parallel combinations of inductors are shown in Figure 4-4 and
Figure 4-5, respectively.
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• In this exercise, you determined the equivalent circuit
inductance for parallel and series combinations of inductors
using the formulas for equivalent inductance.
• You also combined the use of these formulas with
measurements of circuit voltages, currents, and inductive
reactance.
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• When you have completed this exercise, you will be able to measure and
demonstrate inductive phase shift.
• You will also observe the instances of positive and negative power in the power
waveform of reactive ac circuits.
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• As you saw in previous units, the voltage and current waveforms in
resistive ac circuits are in phase, and the power dissipated by resistors
is active power in the form of heat.
• Now, just like the case when capacitance is present in an ac circuit,
there is a phase shift between voltage and current because of
inductance.
• This phase shift is caused by the opposition of inductors to current
changes.
• When current flowing in an inductor starts to change, the inductor
reacts by producing a voltage that opposes the current change.
• The faster the current changes, the greater the voltage produced by the
inductor to oppose the current change.
• In other words, the voltage across the inductor is proportional to the
rate of change in current.
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• Now, suppose that a sine-wave current flows in an inductor.
• At the instant the current goes through a minimum value (negative peak
value), the current is no longer changing and the inductor voltage is
zero since the current rate of change is zero.
• Then, when the current is going to zero amplitude, its rate of change is
maximum and the inductor voltage is maximum.
• As a result, the current in an ideal inductor lags the voltage by 90°.
• The inductive phase shift of 90° between current and voltage is shown
in Figure 4-8.
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• As mentioned earlier in Unit 2, reactive components that cause a phase
shift between circuit voltage and current produce instantaneous power
waveforms having negative and positive values, meaning that power
goes back and forth between the source and the reactive component.
• The instantaneous power waveform for a purely inductive ac circuit is
shown in Figure 4-9.
• This waveform also has equal areas of positive and negative power,
like that for a purely capacitive ac circuit, and the average power over a
complete period is zero.
• However, as you will see in this exercise, real inductors have some
resistance and they will consume a small amount of active power.
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• Consequently, positive and negative areas in the power waveform will
not be exactly equal.
• Note that the instantaneous power waveform frequency is twice the ac
source frequency.
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• In this exercise, you determined inductive phase
shift in an ac circuit using measurements of the
current and voltage waveforms.
• You demonstrated that some active power is
dissipated in inductive circuits because of the
resistance of the inductor wire.
• Finally, observation of the circuit waveforms
allowed you to confirm the theoretical behavior of
the circuit current and voltage.
