You construct a capacitor using a Pyrex drinking glass. The glass is L = 18 cm t

Question

You construct a capacitor using a Pyrex drinking glass. The glass is L = 18 cm tall with an inner radius of r_1 = 3.7 cm and an outer radius of r_2 = 3.9 cm. You line the inside and outside curved surfaces with aluminum foil to act as the plates. a.) Find the equation for the capacitance of your home-made cylindrical capacitor. (For simplicity, you may assume that the glass is long enough that the field is reasonably similar to that seen in an infinitely long one.) Then evaluate your expression to find the capacitance numerically: b.) Using your expression, find the capacitance again after the following construction changes were made. using a larger drinking glass, with the same height but with the inner and outer radii both doubled. stacking two drinking glasses (from part a) on top of each other.

Explanation / Answer

a)The capacitance of cylindrical capacitor is given by:

C = 2 pi k epsilon0 L / ln(r2/r1)

k(pyrex) = 4.5

C = 2 x 3.14 x 8.85 x 10^-12 x 4.6 x 0.18 /ln (0.039/0.037) = 855.97 pF

Hence, C = 855.97 pF

b)Now, r2 = 2 x 0.039 = 0.078 ; r1 = 2 x 0.037 = 0.074

C = 2 x 3.14 x 8.85 x 10^-12 x 4.6 x 0.18 /ln (0.078/0.074) = 855.97 pF

Hence, C = 855.97 pF (remains same)

c)when we stack them, the capacitors are in series,

Ceq = 855.97 x 855.97/(855.97 + 855.97) = 427.96 pF

Hence, C = 427.96 pF

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