3) Consider a cylindrical capacitor with inner radius a= 12.0 cm, outer radius b

Question

3) Consider a cylindrical capacitor with inner radius a= 12.0 cm, outer radius b=14.0 cm, and length L-53.0 cm. A dielectric with dielectric constant k 13.0 fills the volume between the two cylinders. The capacitor is connected to a 110.0 V bat- tery and charged completely. (a) What is the charge on the capacitor? (b) We disconnect the capacitor from the battery- the capacitor is till charged - we take off the dielectric material and we put in place a 0.2 resistor that connects the two cylinders. What is the voltage between the two cylinders? dielectne 7

Explanation / Answer

(A) cylindrical capacitor,

C = 2 pi e0 L / ln(b/a)

C = (2 x pi x 8.854 x 10^-12 x 0.53) / ln(0.14/0.12)

C = 191.3 x 10^-12 F

with dielectric, C' = k C = 2.49 x 10^-9 F

Q = C' V = 273.5 x 10^-9 C .........Ans

(B) now C = 191.3 x 10^-12 F

V' = Q / C = 1430 Volt ....Ans

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