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Subelement E5
ELECTRICAL PRINCIPLES
Section E5D
AC and RF energy in real circuits: skin effect; electrostatic and electromagnetic fields; reactive power; power factor; electrical length of conductors at UHF and microwave frequencies
What is the result of skin effect?
  • As frequency increases, RF current flows in a thinner layer of the conductor, closer to the surface
  • As frequency decreases, RF current flows in a thinner layer of the conductor, closer to the surface
  • Thermal effects on the surface of the conductor increase the impedance
  • Thermal effects on the surface of the conductor decrease the impedance

The AC current density is strongest at the surface of a conductor, and the magnitude decreases exponentially as you get farther away from the surface. Several variables affect this distribution, with frequency being one of them. You just have to remember that the current density at the surface increases with increasing frequency, leading to a 'thinner' RF current.

The skin effect governs how far RF signals penetrate a given material. This is why microwaving certain thicker foods often results in a cold spot in the center!

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Why is it important to keep lead lengths short for components used in circuits for VHF and above?
  • To increase the thermal time constant
  • To avoid unwanted inductive reactance
  • To maintain component lifetime
  • All of these choices are correct

Any wire has self inductance, which increases with the length of the wire (among other things). Since the impedance of an inductor is proportional to frequency, it is usually safe to ignore the self inductance of short wires at low frequencies. But for VHF and above a wire's self inductance may have significant inductive reactance. This reactance is often unwanted and can be minimized by keeping connections short.

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What is microstrip?
  • Lightweight transmission line made of common zip cord
  • Miniature coax used for low power applications
  • Short lengths of coax mounted on printed circuit boards to minimize time delay between microwave circuits
  • Precision printed circuit conductors above a ground plane that provide constant impedance interconnects at microwave frequencies

Microstrip is an RF transmission line implemented on a PCB. Two conductor transmission lines (like coaxial cable) consist of two conductors separated by a dielectric. In a microstrip transmission line the two dielectrics are etched copper layers on the PCB. One is a narrow strip (trace) the other is a wide region of copper (ground plane). The dielectric is the material separating the layers of the PCB, for example FR-4.

See: https://en.wikipedia.org/wiki/Microstrip

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Why are short connections necessary at microwave frequencies?
  • To increase neutralizing resistance
  • To reduce phase shift along the connection
  • Because of ground reflections
  • To reduce noise figure

The answer is somewhat bogus as with microstrip and other high frequency designs, you use controlled lengths of connections (transmission lines) to purposely introduce phase shift which is part of tuning and matching.

In other words, short connections are not necessary other than to cut down on loss and parasitic radiation.

But if you wanted to minimize phase shift (which is rarely a design goal), then you would want short connections.

Just remember it is the only answer with "phase shift" in it.

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Which parasitic characteristic increases with conductor length?
  • Inductance
  • Permeability
  • Permittivity
  • Malleability

Permeability = ability of a material to store energy in a magnetic field

Permittivity = ability of a material to store energy in a electric field

Inductance = a measure of a component's ability to store energy in a magnetic field.

Because wire has permeability we can measure its inductance in terms of - say - microhenries per inch. So, as a conductor gets longer its inductance increases and this is a called a parasitic inductance.

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In what direction is the magnetic field oriented about a conductor in relation to the direction of electron flow?
  • In the same direction as the current
  • In a direction opposite to the current
  • In all directions; omni-directional
  • In a direction determined by the left-hand rule

The Left-Hand Rule:

First point your thumb up, your index finger forward and your middle finger to the right. Your index finger is now pointing in the direction of the magnetic field, your middle finger is pointing in the direction of current (from - to +), and your thumb shows the direction of the force exerted.

This determines that the magnetic field is at 90 degrees to the electron flow in this question. As that is not an option, " In a direction determined by the left-hand rule" would be the only correct answer.

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What determines the strength of the magnetic field around a conductor?
  • The resistance divided by the current
  • The ratio of the current to the resistance
  • The diameter of the conductor
  • The amount of current flowing through the conductor

Biot-Savart law for a sufficiently long wire is: \[B=\frac{\mu I}{2\pi r}\] where:

  • \(B\) is the magnetic field
  • \(\mu\) is the magnetic constant
  • \(r\) is the distance from the wire
  • \(I\) is the current

The direction of the magnetic field \(B\) is found with the right hand rule. The magnetic field is therefore linearly related to the current in the wire.

This section of Wikipedia is helpful : https://en.wikipedia.org/wiki/Magnetic_field#Magnetic_field_and_electric_currents

Also note the right hand rule is for movement of positive charge, and the left hand rule for electron flow. The sign of the charge carrier determines which hand to use. Be positive before you write something down and leave the negativity to the sinister.

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What type of energy is stored in an electromagnetic or electrostatic field?
  • Electromechanical energy
  • Potential energy
  • Thermodynamic energy
  • Kinetic energy

Potential energy is stored energy, so the operative word in the question is, "stored."

Kinetic energy, on the other hand, is energy something moving has. Nothing is moving in an electromagnetic or electrostatic field, so it's got to be stored energy, hence Potential. Indeed, "static" means "not moving."

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What happens to reactive power in an AC circuit that has both ideal inductors and ideal capacitors?
  • It is dissipated as heat in the circuit
  • It is repeatedly exchanged between the associated magnetic and electric fields, but is not dissipated
  • It is dissipated as kinetic energy in the circuit
  • It is dissipated in the formation of inductive and capacitive fields

The question states both ideal inductors and capacitors, so think perfect. The current just passes from the inductors (magnetic field) to the capacitors (electric field), back and forth so none of the power is lost or dissipated.

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How can the true power be determined in an AC circuit where the voltage and current are out of phase?
  • By multiplying the apparent power times the power factor
  • By dividing the reactive power by the power factor
  • By dividing the apparent power by the power factor
  • By multiplying the reactive power times the power factor

The true power in an AC circuit can be determined by multiplying the apparent power times the power factor. The power equation based on Ohm's law assumes that the voltage and current are in phase. Therefore when the voltage and current are out of phase, the result of the power equation is multiplied by a coefficient known as the power factor.

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What is the power factor of an R-L circuit having a 60 degree phase angle between the voltage and the current?
  • 1.414
  • 0.866
  • 0.5
  • 1.73

The power factor of an R-L circuit having a 60° phase angle between the voltage and the current is simply the cosine of that phase angle:

\[\cos{60^{\circ}} = 0.5\]

WARNING: Be careful that your calculator is not in radians; it must be in degrees.

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How many watts are consumed in a circuit having a power factor of 0.2 if the input is 100-VAC at 4 amperes?
  • 400 watts
  • 80 watts
  • 2000 watts
  • 50 watts

Given:
\(E = 100 \text{ V}\)
\(I = 4 \text{ A}\)
Power Factor (\(\text{PF}\)) \(= 0.2\)

How many watts are consumed in this circuit?

The consumption with a power factor of 1.0 would be defined by Ohm's law: \begin{align} P &= E \cdot I\\ &= 100 \text{ V} \cdot 4 \text{ A} \\ &= 400 \text{ W} \end{align}

We call this result the Apparent Power, and often refer to it with the symbol \(S\):
\[S = P_{\text{apparent}}= 400\text{ W}\]

To determine the real power, the apparent power needs to be multiplied by the power factor:
\begin{align} P_{\text{Real}}&= S \cdot \text{PF}\\ &= 400\text{ W} \cdot 0.2 = 80\text{ W} \end{align}

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How much power is consumed in a circuit consisting of a 100 ohm resistor in series with a 100 ohm inductive reactance drawing 1 ampere?
  • 70.7 Watts
  • 100 Watts
  • 141.4 Watts
  • 200 Watts

Only resistance (real component of impedance) consumes power. The values for the resistor, 100 ohms, and current, 1 A, are given.

\begin{align} P_{\text{real}} &= I^2 R\\ &= (1 \text{ A})^2(100 \:\Omega)\\ &= 100 {\text{ W}} \end{align}

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What is reactive power?
  • Wattless, nonproductive power
  • Power consumed in wire resistance in an inductor
  • Power lost because of capacitor leakage
  • Power consumed in circuit Q

Capacitors resist change in voltage and inductors resist change in current each by storing energy and releasing it as voltage and current fluctuate. This is called reactance. Unlike with resistance, no actual power is dissipated by reactance. In purely reactive circuits there will still be measurable voltage and current. The product of this voltage and current is called "wattless" power, measured in volt-ampere reactive (VAR).

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What is the power factor of an R-L circuit having a 45 degree phase angle between the voltage and the current?
  • 0.866
  • 1.0
  • 0.5
  • 0.707

The power factor is defined as the ratio of active (true) power P to the absolute value of apparent power S, or

\[\text{PF} = \frac{P}{|S|}\]

which is also the ratio represented by the cosine of phase angle between the corresponding voltage and current. Therefore, the power factor in this case is

\[\text{PF} = \cos(45^{\circ}) = \frac{\sqrt{2}}{2}\approx0.707\]

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What is the power factor of an R-L circuit having a 30 degree phase angle between the voltage and the current?
  • 1.73
  • 0.5
  • 0.866
  • 0.577

The power factor of an RL circuit having a 30 degree phase angle between the voltage and the current is 0.866.

The power circle equation based on Ohm's law recognizes that the power factor is 1 when there is no phase angle between the voltage and the current.

Therefore taking the trigonometric cosine of the phase angle will give the power factor.

So for this question: \(\cos(30^\circ)=\frac{\sqrt{3}}{2} \approx 0.866\)

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How many watts are consumed in a circuit having a power factor of 0.6 if the input is 200VAC at 5 amperes?
  • 200 watts
  • 1000 watts
  • 1600 watts
  • 600 watts

The power factor \(\text{PF}\) multiples the power. We know that power can be calculated by multiplying the voltage \(V\) and the current \(I\).

\begin{align} \text{Power Consumed} &= V\times I \times\text{PF} \\ &= 200\:\text{V} \times 5\:\text{A} \times 0.6 \\ &= 1000\:\text{W}\times 0.6 \\ &= 600 \:\text{W} \end{align}

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How many watts are consumed in a circuit having a power factor of 0.71 if the apparent power is 500VA?
  • 704 W
  • 355 W
  • 252 W
  • 1.42 mW

In a circuit having a power factor of 0.71 and apparent power of 500 VA, 355 W will be consumed.


\begin{align} \text{Power}_{\text{consumed}} &= \text{Power}_{\text{apparent}} \times \text{Power Factor}\\ &= 500 \times 0.71\\ &= 355\text{ W} \end{align}

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