A typical AAA battery has stored energy of about 3400 J. (Battery capacity is ty

Question

A typical AAA battery has stored energy of about 3400 J. (Battery capacity is typically listed as 625 mA h, meaning that much charge can be delivered at approximately 1.5 V.) Suppose you want to build a parallel plate capacitor to store this amount of energy, using a plate separation of 0.83 mm and with air filling the space between the plates.
a) Assuming that the potential difference across the capacitor is 1.5 V, what must the area of each plate be?

b) Assuming that the potential difference across the capacitor is the maximum that can be applied without dielectric breakdown occurring, what must the area of each plate be?

I know that part A is 2.834×1011 m^2 but I cant figure out part b.

Explanation / Answer

Since you already are ok on part A, I will just focus on part B

What you need to know for part B is the Dielectric Strength for Air. That value is probably in your text somewhere. It is 3 X 106 V/m. If the spacing is .83 mm, then

V = (3 X 106)(8.3 X 10-4) = 2490 V

Since you know the voltage now, its the same thing you did in part A

Energy = .5CV2

3400 = (.5)(C)(2490)2

C = 1.10 X 10-3 F

C = oA/d

A = Cd/o

A = (1.10 X 10-3)(8.3 X 10-4)/(8.85 X 10-12)

A = 1.03 X 105 m2

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