You make a capacitor by cutting the 13.5-cm-diameter bottoms out of two aluminum

Question

You make a capacitor by cutting the 13.5-cm-diameter bottoms out of two aluminum pie plates, separating them by 3.55 mm , and connecting them across a 6.00-V battery.

Part A

What’s the capacitance of your capacitor?

Express your answer with the appropriate units.

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Part B

If you disconnect the battery and separate the plates to a distance of 3.50 cmwithout discharging them, what will be the potential difference between them?

Express your answer with the appropriate units.

Explanation / Answer

1.

C = e0*A/d

e0 = 8.85*10^-12

A = pi*r^2 = pi*(13.5*10^-2)^2/4 = 0.0143 m^2

d = 3.55*10^-3 m

S0,

C = 8.85*10^-12*0.0143/(3.55*10^-3)

C = 35.65*10^-12 F = 35.65 pF

2.

Initially

Q = C*V = 35.65*10^-12*6 = 2.139*10^-10 C

Now new C will be

C1 = 8.85*10^-12*0.0143/(3.5*10^-2) = 3.62*10^-12 F

C1 = 3.62 pF

Now since charge is conserved, So new V will be

V1 = Q/C1

V1 = 2.139*10^-10/(3.62*10^-12) = 59.08 V

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