Clearly a decrease in thickness of the dielectric increases capacitance, but how about the metal plates on a parallel plate capacitor? If you increase or decrease the thickness too much will you see a increase/decrease in capacitance? Is there an optimal thickness of the metal plates?
Electronic – What effect does the thickness of metal plates have on capacitance
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\$\epsilon_r\$ of 2 is kind of small for plastics, a lot are more like 3 or 4, but that's not too important.
As to why it (sort-of) doubles- think about the physical arrangement. The second sheet of plastic (the one that is not between the metal sheets) is doing nothing before you roll it up. When you roll it up, into (say) n turns, you will be using both sides of each sheet of metal, except for the last turn inside and the first turn outside. So, if n is big enough, it approximately doubles (if the roll starts at zero radius, the inside turn won't matter).
You should be able to estimate the radius easily from the standard mensuration formulas for solids. The rectangular prism will have volume of \$V_p = 2t\cdot L\cdot W\$ where t is the thickness of a single sheet of plastic. The cylinder will have a volume of \$V_c = \pi r^2 \cdot L_C\$ where \$L_C\$ is the length of the cylinder. So, depending on how you roll (so to speak), \$L_C\$ will be either L or W from the sheet and by equating the volumes, you can solve for r (which assumes that the inner radius is zero).
This gives the formula and takes account of stacked layers (n). Every odd plate is connected to one capacitor terminal and every even layer connects to the other terminal.
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Best Answer
Think of metal film capacitors which literally have a metal film vapor deposited onto the dielectric. The less metal thickness the less the waste in mass and bulk and metal. It only needs to be thick enough to have full conductivity. Adding thickness just adds mass and bulk with no gain, so optimal thickness is to be as thin as possible.
Note that metal plates need to be thick enough to hold their own weight and shape, as in old style air-gap adjustable capacitors. The plates were about 5 mils thick.
Note that high-energy capacitors for arc simulation will use a thick dielectric with metal foil, soaked in a light oil as a coolant and to prevent internal arcing. These capacitors can be the size of a shoe-box to the size of a filing cabinet, so you just accept their size and weight, normally not portable at all.
What does affect capacitance is the thickness of the dielectric, so the thinner the better, but it must be thick enough to block/handle the rated voltage. More metal (and dielectric) in terms of windings also increases capacitance.
I am sure you have noticed that for a given voltage, more capacitance means a larger capacitor. If the voltage is fixed but you increase capacitance, you have a larger capacitor. For this reason capacitor manufactures offer electrolytics in both tall and skinny, as well as short and fat styles. Most designs make use of some compromise between too much height or too much width, then they chose parts that fit that style.
This is where the compactness of todays capacitors pay off with smaller foot-prints on the board.