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Subelement G5
Electrical Principles
Section G5A
Reactance; inductance; capacitance; impedance; impedance matching
What is impedance?
• The electric charge stored by a capacitor
• The inverse of resistance
The opposition to the flow of current in an AC circuit
• The force of repulsion between two similar electric fields

(C). Impedance is the opposition to the flow of current in an AC circuit. Impedance is composed of resistance and reactance (both capacitive and inductive).

Note: Think that "impedance" is going to "impede" or get in the way of current flow.

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What is reactance?
• Opposition to the flow of direct current caused by resistance
Opposition to the flow of alternating current caused by capacitance or inductance
• A property of ideal resistors in AC circuits
• A large spark produced at switch contacts when an inductor is de-energized

(B). Reactance is the opposition to the flow of alternating current caused by capacitance or inductance. Reactance changes with both the capacitance and inductance of the current to act along with resistance as components of the impedance.

Note: Reactance (either from changes in capacitance and/or inductance) is going to make the circuit "react" and block (oppose) current flow in the AC circuit.

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Which of the following causes opposition to the flow of alternating current in an inductor?
• Conductance
• Reluctance
Reactance

(D). Reactance is the factor listed which causes opposition to the flow of alternating current (AC) in an inductor. Both inductive (from an inductor) and capacitive (from a capacitor) reactances act with resistance to oppose the flow of current as components of impedance.

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Which of the following causes opposition to the flow of alternating current in a capacitor?
• Conductance
• Reluctance
Reactance

(C). The Reactance is the factor which causes opposition to the flow of alternating current (AC) in a capacitor. Both capacitive (from a capacitor) and inductive (from an inductor) reactances along with resistance combine as the impedance causing the opposition to the flow of AC current through the circuit.

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How does an inductor react to AC?
• As the frequency of the applied AC increases, the reactance decreases
• As the amplitude of the applied AC increases, the reactance increases
• As the amplitude of the applied AC increases, the reactance decreases
As the frequency of the applied AC increases, the reactance increases

Reactance — whether inductive or capacitive — opposes the flow of current. Inductive reactance varies proportionately with the frequency, so as frequency increases, the inductive reactance also increases.

(Capacitive reactance varies inversely with frequency.)

Notice that the equation for inductive reactance is defined with frequency, not amplitude:

$X_L = 2\pi{f}L$

\begin{align} X_L & = \text{Inductive reactance}\\ \pi & = \text{pi (3.14159...)}\\ f & = \text{Frequency}\\ L & = \text{Inductance}\\ \end{align}

The amplitude of the applied AC has no effect on reactance, eliminating two distractors.

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How does a capacitor react to AC?
As the frequency of the applied AC increases, the reactance decreases
• As the frequency of the applied AC increases, the reactance increases
• As the amplitude of the applied AC increases, the reactance increases
• As the amplitude of the applied AC increases, the reactance decreases

As the frequency of the AC current applied to a capacitor increases, the reactance of the capacitor decreases.

The capacitive reactance is inversely proportional to the frequency. The higher the frequency of the AC current, the less charge can accumulate in the capacitor, and so the opposition to the current decreases.

Given:
$\pi$ = pi (3.14…)
$f$ = frequency
$C$ = Capacitance

$\text{Capacitive Reactance }(X_C) = \frac{ 1 }{ 2\pi{f}C }$

From the equation, one can see that as the frequency increases, the reactance of the capacitor decreases.

From Wikipedia:
Reactance is the opposition of a circuit element to a change of electric current or voltage, due to that element's inductance or capacitance. A built-up electric field resists the change of voltage on the element, while a magnetic field resists the change of current. The notion of reactance is similar to electrical resistance, but they differ in several respects.

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What happens when the impedance of an electrical load is equal to the output impedance of a power source, assuming both impedances are resistive?
• The source delivers minimum power to the load
• The electrical load is shorted
• No current can flow through the circuit
The source can deliver maximum power to the load

(D). When the impedance of an electrical load is equal to the internal impedance of the power source, the source can deliver maximum power to the load. When the impedances are equal they are said to be "matched". For both AC and DC currents matching the impedances causes the reactance of the system to be negligible or ideally, zero. This allows for maximum flow of current.

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What is one reason to use an impedance matching transformer?
• To minimize transmitter power output
To maximize the transfer of power
• To reduce power supply ripple

(B). One reason to use an impedance matching transformer is to maximize the transfer of power. This type of transformer alters the current and voltages, which changes the impedances between the power source and load. Matching the impedances allows for maximum power transfer, so this is one component which may be used for the function.

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What unit is used to measure reactance?
Ohm
• Ampere
• Siemens

The ohm (Ω) is the unit used to measure Reactance. The ohm is also the unit for electrical Impedance and Resistance, as these are all related properties that impede the flow of current in an AC circuit.

Resistance This is essentially friction against the flow of current. It is present in all conductors to some extent (except superconductors!), most notably in resistors. When the alternating current goes through a resistance, a voltage drop is produced that is in phase with the current. Resistance is mathematically symbolized by the letter “R” and is measured in the unit of ohms (Ω).

Reactance This is essentially inertia against the flow of current. It is present anywhere electric or magnetic fields are developed in proportion to an applied voltage or current, respectively; but most notably in capacitors and inductors.

When the alternating current goes through a pure reactance, a voltage drop is produced that is 90° out of phase with the current. Reactance is mathematically symbolized by the letter “X” and is measured in the unit of ohms (Ω).

Impedance This is a comprehensive expression of any and all forms of opposition to current flow, including both resistance and reactance. It is present in all circuits, and in all components.

When the alternating current goes through an impedance, a voltage drop is produced that is somewhere between 0° and 90° out of phase with the current. Impedance is mathematically symbolized by the letter “Z” and is measured in the unit of ohms (Ω), in complex form.

Perfect resistors possess resistance, but not reactance. Perfect inductors and perfect capacitors possess reactance but no resistance. All components possess impedance, and because of this universal quality, it makes sense to translate all component values (resistance, inductance, capacitance) into common terms of impedance as the first step in analyzing an AC circuit.

Review of R, X, and Z (Resistance, Reactance, and Impedance)

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Which of the following devices can be used for impedance matching at radio frequencies?
• A transformer
• A Pi-network
• A length of transmission line
All these choices are correct

All of the choices are correct. All of the listed devices are ones that can be used to match the impedances of the circuit frequency. Impedance matching is important as it allows for maximum transfer of power from the source to the load.

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Which of the following describes one method of impedance matching between two AC circuits?
Insert an LC network between the two circuits
• Reduce the power output of the first circuit
• Increase the power output of the first circuit
• Insert a circulator between the two circuits

Though impedance matching is typically done with a balun, it is important to understand how other components will affect an antenna circuit. In this question, you can rule out the distractors of increasing or decreasing the power as these are not impedance matching. A circulator is typically a diode based device and therefore does not effect impedance. An LC Network contains an inductor (L) and capacitor (C). The key is the inductor as this component affects impedance. The correct answer is Insert an LC Network between the two circuits.