A parallel plate capacitor is made by having plates which are square, with a siz

Question

A parallel plate capacitor is made by having plates which are square, with a size of   2.84 mm    on each size. They are initially a distance   1.03 mm    apart from each other. What is the capacitance of this capacitor?

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Part B

The separation between the plates is increased to   6.31 mm   . What is the capacitance now?

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Part C

If we pulled apart the plates while the capacitor was connected to a   7.10 V    battery, what is DIFFERENCE between the initial charge on the capacitor and the final charge on the capacitor?

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Part D

If we pulled apart the plates while the capacitor was connected to a   7.10 V    battery, what is DIFFERENCE between the initial energy stored in the capacitor and the final energy stored in the capacitor?

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Part E

Now imagine that we again started with the capacitor plates at distance   1.03 mm    hooked up to a battery at potential   7.10 V   . However, we disconnected the battery before moving the places to   6.31 mm   . What is the DIFFERENCE between the initial and final potentials?

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Part F

Now imagine that we again started with the capacitor plates at distance   1.03 mm    hooked up to a battery at potential   7.10 V   . However, we disconnected the battery before moving the places to   6.31 mm   . What is the DIFFERENCE between the initial and final potential energy stored in the capacitor?

Explanation / Answer

area of plates = A = (2.84*10^(-3))^2 = 8.065*10^(-6) m^2

separation between plates = d = 1.03*10^(-3) m

a)

capacitance C = e0*A/d = 8.85*10^(-12)*8.065*10^(-6)/(1.03*10^(-3)) = 6.93*10^(-14) F

b)

new d = 6.31*10^(-3) m

new capacitance C(new) = 8.85*10^(-12)*8.065*10^(-6)/(6.31*10^(-3)) = 1.13*10^(-14) F

c)

Qi = C*V = 6.93*10^(-14)*7.1 = 4.92*10^(-13) C

Qf = C(new)*V = 1.13*10^(-14)*7.1 = 8.02*10^(-14) C

Qi - Qf = 4.92*10^(-13) - 0.802*10^(-13) = 4.12*10^(-13) C

d)

Ui = (1/2)*C*V^2 = 0.5*6.93*10^(-14)*7.1^2 = 1.74*10^(-12) J

Uf = (1/2)*C(new)*V^2 = 0.5*1.13*10^(-14)*7.1^2 = 2.85*10^(-13) J

Ui - Uf = 1.74*10^(-12) - 0.285*10^(-12) = 1.45*10^(-12) J

e)

C = e0*A/d = 8.85*10^(-12)*8.065*10^(-6)/(1.03*10^(-3)) = 6.93*10^(-14) F

Vi = 7.1 volt

Q = C*V = 6.93*10^(-14)*7.1 = 4.92*10^(-13) C

new C = e0*A/d = 8.85*10^(-12)*8.065*10^(-6)/(6.31*10^(-3)) = 1.13*10^(-14) F

new voltage Vf = Q/C = 4.92*10^(-13)/(1.13*10^(-14)) = 43.54 volt

Vi - Vf = 7.1 - 43.54 = - 36.44 volt

f)

Ui = (1/2)*C*Vi^2 = 0.5*6.93*10^(-14)*7.1^2 = 1.74*10^(-12) J

Uf = (1/2)*C(new)*Vf^2 = 0.5*1.13*10^(-14)*36.44^2 = 7.5*10^(-12) J

Ui - Uf = 1.74*10^(-12) - 7.5*10^(-12) = - 5.76*10^(-12) J

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