Consider a plane parallel-plate capacitor made of two strips of aluminum foil se

Question

Consider a plane parallel-plate capacitor made of two strips of aluminum foil separated by a layer of paraffin-coated paper. Each strip of foil and paper is 7. 60 cm wide. The foil is 0. 00400 mm thick, and the paper is 0. 0300 mm thick and has a dielectric constant of 3. 70. What length should the strips be if a capacitance of 6. 00 times 10-8 F is desired? (If, after the: plane capacitor is formed, a second paper strip can be added below the foil-paper-foil stack and the resulting assembly rolled into a cylindrical form-similar to that shown in the figure below-the capacitance can be doubled because both surfaces of each foil strip would then store charge. Without the second strip of paper, however, rolling the layers would result a short circuit. )

Explanation / Answer

capacitance = K E A / d

where K is dielec const, E is epsilon naught, A is area of a foil stripand d is the thickness of the paper

So...

C = K E width * L / d

or

L = C d / K E width = 6.00x10^-8 * 3x10^-5 / 3.70 * 8.85x10^-12 * 0.076 =

= 0.7233 m

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