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 3200.0 mu F and is charged to a potential difference of 66.0 V. Calculate the amount of energy stored in the capacitor. Calculate the charge on this capacitor when the electrical energy stored in the capacitor is 8.29 J. If the two plates of the capacitor have their separation increased by a factor of 6 while the charge on the plates remains constant, by what factor is the energy stored in the capacitor increased?

Explanation / Answer

here,

capacitance , C = 3200 uF

potential difference , V = 66 V

the energy stored in the capacitor , E = 0.5 * C * V^2

E = 0.5 * 3200 * 10^-6 * 66^2 J

E = 6.97 J

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let the charge be Q

0.5 * Q^2 /C = E

0.5 * Q^2 / (3200 * 10^-6) = 8.29

Q = 0.23 C

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when d' = 6 d

the new capacitance , C' = area * e0 /d' = C/6

the energy stored , E' = 0.5 * Q^2 /C'

E' = 0.5 * Q^2 /(C/6) = 6 * E

so, the energy stored is also increased by a factor of 6   

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