A capacitor consists of two closely spaced metal conductors of large area, separ

Question

A capacitor consists of two closely spaced metal conductors of large area,
separated by a thin insulating foil. It has an electrical capacity of
3800  uF and is charged to a potential difference of 84.0 V.

1) Calculate the amount of energy stored in the capacitor.

2) Calculate the charge on this capacitor when the electrical energy stored in the capacitor is 9.85J.

3) If the two plates of the capacitor have their separation increased by a factor of 8 while the charge on the plates remains constant, by what factor is the energy stored in the capacitor increased?

The first part has been answered on this link: https://www.chegg.com/homework-help/questions-and-answers/capacitor-consists-two-closely-spaced-metal-conductors-large-area-separated-thin-insulatin-q7881003

I only need the answers to parts 2 & 3, please. Thanks.

Explanation / Answer

1) energy stored is U = 0.5*C*V^2 = 0.5*3800*10^-6*84^2 = 13.4 J

2) U = Q^2/(2*C)

9.85 = Q^2/(2*3800*10^-6)

Q = sqrt(9.85*2*3800*10^-6) = 0.273 C

3) by increasing the seperation between the plates by 8 times

From C = eo*A/d

C1*d1 = C2*d2

C2 = C1*d1/d2 = C1*d1/(8*d1) = C1/8 = (3800*10^-6)/8 = 4.75*10^-4 F

then U2 = Q^2/(2*C2) = Q^2/(2*(C1/8)) = 8*Q^2/(2*C1) = 8*U1

Energy stored increases by 8 times

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