A parallel-plate capacitor has a capacitance of 25 F when filled with air and it

Question

A parallel-plate capacitor has a capacitance of 25 F when filled with air and it can withstand a potential difference of 50 V before it suffers electrical breakdown.

(a) What is the maximum amount of charge we can place on this air-filled capacitor? The dielectric strength of air is 3.0 x 10^6 V/m.

(b) If we fill this capacitor with polyethylene, what will be its new capacitance?

(c) What will be the maximum potential difference that this new capacitor can withstand? What will be the corresponding maximum amount of charge we can place on this capacitor? The dielectric strength of polyethylene is 18 x 10^6 V/m.

Explanation / Answer

capacitance C = 25 µF = 25 * 10 ^-6 F potential difference V = 50 V (a) The maximum amount of charge we can place on this air-filled capacitor Q = CV = 1.25 * 10 ^-3 coulomb (b). The dielectric strength of air E = 3.0 x 10^6 V/m. The dielectric strength of polyethylene E ' = 18 x 10^6 V/m dielctric constant of polyethylene K = E ' / E = 3 new capacitance C ' = KC = 75 uF = 75 * 10 ^-6 F (c) the maximum potential difference that this new capacitor can withstand V ' = V = 50 V the corresponding maximum amount of charge Q ' = C ' V ' = 3.75 * 10 ^-3 coulomb

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