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Subelement G5

ELECTRICAL PRINCIPLES

Section G5A

Reactance; inductance; capacitance; impedance; impedance transformation; resonance

What happens when inductive and capacitive reactance are equal in a series LC circuit?

  • Resonance causes impedance to be very high
  • Impedance is equal to the geometric mean of the inductance and capacitance
  • Correct Answer
    Resonance causes impedance to be very low
  • Impedance is equal to the arithmetic mean of the inductance and capacitance

Capacitive reactance is a negative imaginary component and inductive reactance is a positive imaginary component--thus, when they are equal, they cancel each other out, leaving the impedance equal to the resistance with no imaginary component. This is the minimum impedance, and thus the condition for resonance.

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What is reactance?

  • Opposition to the flow of direct current caused by resistance
  • Correct Answer
    Opposition to the flow of alternating current caused by capacitance or inductance
  • Reinforcement of the flow of direct current caused by resistance
  • Reinforcement of the flow of alternating current caused by capacitance or inductance

(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.

Hint: Reactance includes the letters "AC"

For more info see Wikipedia: Reactance

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Which of the following is opposition to the flow of alternating current in an inductor?

  • Conductance
  • Reluctance
  • Admittance
  • Correct Answer
    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.

For more info see Wikipedia: Electrical Reactance, Inductor

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Which of the following is opposition to the flow of alternating current in a capacitor?

  • Conductance
  • Reluctance
  • Correct Answer
    Reactance
  • Admittance

(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.

For more info see Wikipedia: Electrical Reactance, Capacitor

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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
  • Correct Answer
    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.

For more info see Wikipedia: Electrical Reactance, Inductor

Silly way to help remember: How does an IN-ductor react to AC? As freq IN-creases, reACtance IN-creases. It's an IN-IN-IN! Also, indUctor goes up (capacitor goes down)

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How does a capacitor react to AC?

  • Correct Answer
    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:
\[ \begin{align} \pi &= 3.14…\\ f &= \text{frequency}\\ C &= \text{Capacitance}\\ \end{align} \]

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

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


SILLY HINT: the band AC/DC - Frequency increases - 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.

For more info see Wikipedia: Electrical Reactance, Capacitor

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What is the term for the inverse of impedance?

  • Conductance
  • Susceptance
  • Reluctance
  • Correct Answer
    Admittance

This is just a definition. To address the distractors:

  • Conductance is the REAL part of the true answer. In other words, conductance is the inverse of Resistance, not impedance.
  • Susceptance is the IMAGINARY part of the true answer. That is, it is the inverse of Reactance as it relates to impedance.
  • Reluctance is the opposition to creating magnetic fields. It really has nothing to do with impedance at all.

The answer is Admittance, which is the vector of both Conductance and Susceptance - two of the distractors.

Hint: Impedance impedes, and the opposite of impeding is admitting.

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What is impedance?

  • The ratio of current to voltage
  • The product of current and voltage
  • Correct Answer
    The ratio of voltage to current
  • The product of current and reactance

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... kinda like Resistance, except it changes with frequency.

You might think of it as resistance due to inductance and capacitance on alternating current. As such, just like with Ohm's law (\(R = \frac{E}{I}\)) the impedance is the ratio of voltage to current (\(\frac{E}{I}\)).

For more info see Wikipedia: Electrical Impedance

SILLY HINT: The correct choice is the only one with VOLTAGE following OF in the wording.

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What unit is used to measure reactance?

  • Farad
  • Correct Answer
    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.

For more info see Wikipedia: Ohm, Electrical Reactance

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
  • Correct Answer
    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.

For more info see Wikipedia: Impedance matching

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What letter is used to represent reactance?

  • Z
  • Correct Answer
    X
  • B
  • Y

This is just a definition - learn that reactance is represented by X. It can’t be Z because Z is impedance.

\[Z = R + X_i\]

That is, impedance equals real resistance plus imaginary reactance.

Mnemonic: If you pronounce reactance with an extended southern drawl, re-act-taance sounds just a little bit more like X than the other possible choices.

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What occurs in an LC circuit at resonance?

  • Current and voltage are equal
  • Resistance is cancelled
  • The circuit radiates all its energy in the form of radio waves
  • Correct Answer
    Inductive reactance and capacitive reactance cancel

Think of inductive reactance as having a positive sign and capacitive reactance having a negative sign. If they are equal, they add to zero (they cancel).

Silly hint: deCAPitate a snake by slicing horizontally (-) across the ground

IndUct (+) goes Up ^

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