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. When the potential difference across the capacitor is 1.5 V, the area of each plate is 2.834×1011 m*m
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?

Explanation / Answer

For air dielectric capacitors, the breakdown electric field strength E is of the order 2 to 5 MV/m, depending on air pressure. Assuming E=3MV/m as typical, then:
V = Vbd = E*d

Then from E=½CV² and C=A/d, we get:
A = 2dE/(V²)

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