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# Capacitor Basics

 MEs, take note!

Capacitors are devices which store electrical energy in the form of an electric field.  The process is quite similar to the way mechanical springs store energy in the form of elastic material deformation, to the extent that the math describing both is quite similar, save for the variables used.  The similarity may in fact be part the reason that students of electrical or mechanical engineering often find the others’ studies arcane and inscrutable; “v” means “voltage” to an EE, but “velocity” to an ME, whose representations of springs may look rather like inductors to an EE, etc.

The concept of the parallel plate capacitor is generally used as the starting point for explaining most practical capacitor constructions.  It consists of two conductive electrodes positioned parallel to each other and separated by an insulator, usually one of several polymers, ceramic materials, metal oxides, air or occasionally a vacuum.

The value of such a capacitor, essentially it’s “spring constant” for the mechanically–minded, is approximated by the formula below when the separation distance between the plates is small relative to their area.  It should be noted however, that mechanical spring constants and capacitor values are, by convention, expressed with reciprocal dimensions; a mechanical spring constant is typically expressed in terms of force per unit of displacement (such as newtons per meter or pounds-force per inch) whereas a capacitance value is expressed in terms of displacement per unit force, i.e. coulombs per volt.

 Where:C = the capacitance of the deviceA = the area of overlap of the two platesd = the distance between the two plates (thickness of the dielectric material)ε0 = the permittivity of free space, which is a physical constantεr = the (relative) dielectric constant of the insulator

Practically speaking, the plates need not be flat; rolled, folded, crumpled, stacked, sliced, diced, and julienned geometries work also, though the math involved can become rather messy as geometries become more complex.

So then, to make a capacitor with a larger value, one can use plates with a larger area, reduce the separation distance (i.e. thickness of the dielectric material) or increase the dielectric constant of the material.  Messing with ε0 pretty much requires the creation of an alternate universe, which is a rather difficult thing to do outside the realm of politics.

But what the heck is this “dielectric constant” thing? Excellent question; it’s essentially a property of materials describing their ability to become electrically polarized in the presence of an applied electric field, through any of a number of mechanisms.  These mechanisms might be at an atomic level, where the cloud of electrons surrounding the nucleus of an atom is displaced, resulting in an atom having a slightly positive charge on one side and corresponding negative charge on another.  It can also occur at a molecular level, due to changes in the orientation of electrically polar molecules in response to an applied field, or through bending & stretching of the bonds between atoms within a molecule, very much like the material in a mechanical spring is bent or stretched.

Provided that the electrons in the atomic case don’t “blow away” and re-associate with an adjacent nucleus,  and in the molecular cases that the molecules aren't torn apart by the force of the electric field, the material functions as an insulator; it doesn't support a sustained flow of charge when an electric field is applied, though it does effectively permit some charge to flow as the field is established, due to the shifting of electrons around an atom or reorientation/distortion of molecules.  Removing the applied electric field allows the electrons in the dielectric to return to their normal distribution around the nuclei to which they’re attached, or the molecules in the substance to return to their original random orientation or shape.  In the process of so doing, most of the charge that flowed through the capacitor when the electric field was applied is returned to the circuit, flowing in the opposite direction.

A material’s (relative) dielectric constant describes the extent to which a material facilitates this temporary current flow, relative to the extent that a vacuum does so.  A material that allows the same amount of charge transfer as a vacuum for a given area, separation distance, and applied field strength has a dielectric constant of 1, a material allowing twice the charge transfer as a vacuum has a dielectric constant of 2, etc.

The nuances of different capacitor types are, for the most part, determined by the characteristics of the dielectric used and the method by which a given device is constructed.  All dielectric materials have limitations, with regard to the maximum applied field they can withstand for a given material thickness, their dielectric constant, losses that occur in the dielectric material and electrodes, and the amount of current that flows or “leaks” through the dielectric when the applied electric field is constant.

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