The parallel plates in a capacitor, with a plate area of 9.20 cm2 and an air-fil

Question

The parallel plates in a capacitor, with a plate area of 9.20 cm2 and an air-filled separation of 2.70 mm, are charged by a 4.60 V battery. They are then disconnected from the battery and pulled apart (without discharge) to a separation of 9.90 mm. Neglecting fringing, find (a) the potential difference between the plates, (b) the initial stored energy, (c) the final stored energy, and (d) the work required to separate the plates. (a) Number (b) Number (c) Number (d) Number Units Units Units Units

Explanation / Answer

here,

plate area , A = 9.2 cm^2 = 9.2 * 10^-4 m^2

initial sepration , d0 = 2.7 * 10^-3 m

final sepration , d = 9.9 mm = 9.9 * 106-3 m

potential difference , V0 = 4.6 V

initial charge , Q = V0 * area * e0 /d0

a)

the potential difference between the plates , V = Q /(area * e0 /d)

V = (V0 /d0 ) /( 1 /d)

V = 4.6 * 9.9 /2.7 V

V = 16.9 V

b)

the initial energy stored , E0 = 0.5 * C0 * V0^2

E0 = 0.5 * ( 9.2 * 10^-4 * 8.85 * 10^-12 /( 2.7 * 10^-3)) * 4.6^2 J

E0 = 3.2 * 10^-11 J

c)

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

E = 0.5 * ( 9.2 * 10^-4 * 8.85 * 10^-12 /( 9.9 * 10^-3)) * 16.9^2 J

E = 1.2 * 10^-10 J

d)

the work required to seprate the plates , W = E - E0

W = 8.8 * 10^-11 J

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