The approximation formula for a powdered-iron toroid is: \[N = 100 \times \sqrt{\frac{L}{A_L}}\]

Where:
\(N\) is the number of turns
\(L\) is the inductance in microhenries
\(A_L\) is the inductance index
     (and must be in microhenries per 100 turns to
      be consistent with the units for \(L\)).

So, \begin{align} N &= 100 \times \sqrt{\frac{L}{A_L}}\\ &= 100 \times \sqrt{\frac{5}{40}}\\ &= 100 \times \sqrt{0.125}\\ &= 35.4\\ &\approx 35\text{ turns} \end{align}

The multiplier for henries in the formula doesn't matter as long as both \(L\) and \(A_L\) use the same multiplier. For example, \(L\) can be henries if \(A_L\) is henries per 100 turns; \(L\) can be millihenries as long as \(A_L\) is millihenries per 100 turns

The only answer with a five (5) so, 5 microhenries = 35 turns. Albert WP4AES

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The correct answer here is that a quartz crystal's equivalent circuit is a series RLC circuit in parallel with a shunt capacitor, \(C_p\), which represents electrode and stray capacitance.

Explanation:

1. Series RLC: The quartz crystal itself can be modeled as a series RLC (resistor-inductor-capacitor) circuit due to the mechanical vibrations it undergoes. The resistance \((R)\) models energy losses, the inductance \((L)\) represents inertia in the crystal's oscillations, and the capacitance \((C)\) is linked to its elasticity.

2. Shunt Capacitance \((C_p)\): This shunt capacitor models the capacitance between the crystal's electrodes and any additional stray capacitance from the surrounding circuit. It is placed in parallel with the series RLC to represent the full behavior of the crystal in a circuit.

3. Resonant Frequencies: This configuration supports two resonance points—series resonance and parallel resonance. At series resonance, the series RLC impedance is at a minimum, and the crystal operates as a low-impedance path. At parallel resonance, the combined effect of the series RLC and \(C_p\) creates a high-impedance path, setting the parallel resonant frequency.

Incorrect answers suggest either purely parallel configurations or series/parallel combinations that don’t match the actual behavior of the crystal's resonant properties.

Memory tips:

1. The only answer that includes the mention of a shunt capacitor is the correct choice.
2. equivalent circuit means a circuit that replaces the quartz crystal.
3. The only correct answer does not include crystal

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Ever used piezo ignition for your gas stove or oven? https://en.wikipedia.org/wiki/Piezo_ignition

This is using the same property: you press a button (usually hard!) to deform a crystal and as a result you get a nice little spark due to a (brief) high voltage.

So if you deform the crystal, you get a voltage. You can also apply a voltage to deform the crystal.

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As a variable inductor is turned, the slug moves into the air space inside the coil, changing its magnetic properties and thus the quantity of inductance. Inserting a ferrite slug increases the inductance. Conversely, a brass slug decreases the inductance as it goes in. Both can be useful in building a tuned circuit. Ferrite is found in all sorts of electromagnetic applications including inductors, transformers, chokes, solenoids, etc.

Cobalt and aluminum are metals but they don't have properties ideal for an inductor. Polystyrene, polyethylene, Teflon, and Delrin are all plastics and wouldn't do anything at all in an inductor.

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Because ferrite toroids have a higher permeability than powdered-iron toroids, the inductance for a given number of turns is increased. Therefore, smaller inductors and inductors with fewer turns are possible using ferrite toroids.

Memory tip:
Ferrite Toroids = Fewer Turns

Hint: 'Inductor' is in the question and 'Inductance' only appears in the correct answer.

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Permeability is a measure of the response of a given material to a magnetic field. The measure is relative to the magnetic field strength observed with no core. A higher permeability will result in a higher inductance for a constant number of turns on the toroid. It is measured in henries per meter. Air has a permeability of 1. So, the permeability of the material used in the core of the toroid will have the biggest impact on its inductance

(The somewhat similar-sounding Permittivity refers to polarization in response to an electric field.)

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This is simply memorizing that toroidal cores support a frequency range up to 300 MHz.

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Powdered-iron cores have better temperature stability but the permeability is lower. Ferrite cores have higher permeability but the temperature stability is not as good. If temperature stability is more important than size, then powdered-iron core may be desirable.

Hint: The "I" in Iron means "I" like the symbol for current measured in amps.

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The ferrite bead (small sphere of ferrite with a hole through it) is a very small core and acts as a filter to suppress higher frequency noise.

https://en.wikipedia.org/wiki/Ferrite_bead

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Because of the circular geometry of the toroidal core, it contains most of the magnetic field inside the core. This makes toroids well suited for use on circuit boards where magnetic field interference with other components is undesirable.

Hint: All answers start with "Toroidal cores". What is important is that the the correct answers' 3rd word comes first alphabetically among all the answers. The "C" in confines is the first alphabetically.

Another hint: the question has the word "core" twice and so does the answer.

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The equation for a ferrite toroid is:

\[N = 1000 \times \sqrt {\frac{L}{A_L}}\]

Where:

\(N\) is the number of turns;
\(L\) is the inductance in millihenries;
\(A_L\) is the inductive index (which must be given in millihenries per 1000 turns for this equation).

So,

\begin{align} N &= 1000 \times \sqrt {\frac{L}{A_L}}\\ &= 1000 \times \sqrt {\frac{1}{523}}\\ &= 43.7\\ &\approx 43\text{ turns} \end{align}

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Ferrite greatly increases the inductance of a coil, allowing the use of smaller coils to do the same job compared to an air-core inductor. But ferrite can only store a limited amount of energy. If too much current is passed through the coil the ferrite will saturate and can't store any additional energy. The inductor then behaves as if the ferrite is not there, with a consequently much lower inductance value, until the energy is drained back out. This is usually bad although specialized applications take advantage of it.

Inductors store current, not voltage, so the answer about voltage is irrelevant. And the two answers about coupling are similar enough that they can't both be right.

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Self-resonance happens when you have both inductance and capacitance in series.

Real world components have parasitics-- every component contains resistance, inductance, and capacitance in addition to the values it is designed to have.

In an inductor, adjacent wire acts similarly to the plates of a capacitor to create a small amount of parasitic capacitance between each turn. This combination of inductance and capacitance causes resonance.

Caution: Distractor Coupling is a general term for a transfer of energy, which may involve inductor fields. It typically refers to connecting two physically separate circuits.

Inter-turn capacitance describes a specific field effect occurring in the inductor, thus it's the most correct answer.

HINT: Both "self-resonance" in the question, and "inter-turn" in the answer, are hyphenated words.

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Ferrite is found in many electromagnetic applications because it increases inductance, allowing smaller, lighter parts to do the same job. Powdered iron fits a similar role, also increasing inductance. Brass is pretty much only used in variable inductors because it reduces inductance compared to the air it displaces as you turn the slug. Normally you'd just make a smaller coil, but sometimes other constraints exist. Ceramic is inert and doesn't do anything. Aluminum is paramagnetic and does not significantly change inductance.

Hint: Slug think bullet and brass is the common casing.

All other factors being equal, the greater the magnetic permeability of the core which the coil is wrapped around, the greater the inductance; the less the permeability of the core, the less the inductance.

Brass is diamagnetic ("anti-magnetic"), and diamagnetic materials have relative permeability less than 1 (free space). Therefore, replacing the air in the coil with brass reduces the relative permeability of the core, reducing its inductance. All of the other materials mentioned will either increase the inductance or leave it unchanged.

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Even if there is no load, a small amount of current flows through a transformer when AC is applied. This current creates a magnetic field, and is called the magnetizing current.

If there is a load on the secondary, it acts to deplete the magnetic field and generally increases the amount of current flowing in the primary beyond the magnetizing current.

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Any kind of circuit that absorbs transient spikes caused by switching action is called a "snubber".

Mnemonic: This circuit "Snuffs out" nubs in the voltage.

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Inductors and transformers frequently have a core made of ferrite because it greatly increases the quantity of inductance compared to an air core. However, the ferrite can only hold a limited amount of energy. Once it is saturated it no longer boosts the inductance of the coil and thus the inductor behaves like a much smaller inductor. This results in a non-linear effect as the threshold is crossed, and any kind of non-linear behavior is sure to cause harmonics and distortion.

Flux, suseptance, and permeability are all words you might see in association with transformers and inductors, however none of them are intrinsically a problem so much as parameters you might measure.

-gxti

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