A commercial capacitor is to be constructed as shown in Figure. This particular capacitor is
made from two strips of aluminum foil separated by a strip of paraffin-coated paper. Each
strip of foil and paper is 7.90 cm wide. The foil is 0.00400 mm thick, and the paper is
0.0250 mm thick and has a dielectric constant of 4.60. What length should the strips have if
a capacitance of 9.50 10-8 F is desired before the capacitor is rolled up? (Adding a second
strip of paper and rolling the capacitor effectively doubles its capacitance by allowing charge
storage on both sides of each strip of foil)
The two very thin strips separated by a strip of dielectric can be considered as a parallel
plate capacitor even if it is rolled and thus the capacitance is given by
Here A is the area of the strips, d is the separation and
dielectric constant of the material separating them. Thus
is the relative permittivity i.e.
As the capacitance is doubled because rolling it with an extra dielectric paper we can write
Or
Or