From Wikipedia:

Piezoelectricity is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress.

The piezoelectric effect is a reversible process: materials exhibiting the piezoelectric effect also exhibit the reverse piezoelectric effect, the internal generation of a mechanical strain resulting from an applied electric field.

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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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When a changing magnetic field interacts with a solid conductor, it induces circulating currents within the conductor. These currents are called eddy currents and they dissipate energy as heat. By using thin layers of magnetic material instead of a solid core, the path for eddy currents is significantly reduced. This is because the current tends to flow in loops, and the thin layers act like many smaller conductors, disrupting these loops and hindering the flow of eddy currents. By minimizing eddy currents, the core experiences less heat generation and overall power loss is reduced. This is crucial for efficient operation of inductors and transformers.

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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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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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High temperature iron powder, as the name suggests, is a specialty powder able to withstand elevated temperatures without degrading. While ordinary iron powders may begin to oxidize or lose their magnetic abilities above 300-400°C, high temp powders resist these changes even beyond 1000°C.

Source: https://am-material.com/news/high-temperature-iron-powder/

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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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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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Saturation of a magnetic material occurs when the metal has absorbed as much of the magnetic field as it can. Thus, an inductor goes into saturation when there is too much magnetic flux for it to absorb.

The permeability of a material does not itself cause saturation, but only changes how much flux is required before it saturates. If you know your magnetic field will never get that strong, then you can safely use a core with a lower permeability.

Saturation is less common at higher frequencies, as the inductor has less time to absorb the magnetic field before the signal reverses. Permittivity is relevant to capacitors and electric fields and has no relevance here.

https://en.wikipedia.org/wiki/Saturation_(magnetic)

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