Capacitor Energy With Different Dielectrics

[recursive]

Homework Statement

Two parallel plates are connected to a battery which maintains a constant potential difference of 12.0 V. The distance between the plates can be varied and there are three plates of different dielectric materials available: rubber (0.40 mm, κ = 6.7), glass (4 mm, κ = 7) and teflon (3 cm, κ = 2.1). The area of the plates is 91 cm². What is the maximum energy that can be stored in the capacitor using one of the three materials?

Homework Equations

C = K*A₀ε₀/d

PE = CV²/2

The Attempt at a Solution

The highest energy stored will be in the system with the greatest capacitance; i.e., where the ratio of K/d is the largest. Rubber's K/d is greater than the other options, so rubber as the dielectric should produce the greatest capacitance.

C = (6.7)(.91)(8.854 * 10^-12) / .0004

C = 1.35 * 10^-7 F

With the capacitance, the energy can be calculated:

PE = CV²/2

PE = (1.35 * 10^-7)(12²)/2

PE = 9.72 * 10^-6 J
This answer isn't correct, and I'm not sure why. My first concern was that I might not have converted all the units appropriately, but I've diligently checked, and I'm pretty sure they are all correct. (But the undying suspicion is that they are not is, well, undying.)

I am assuming I am missing something conceptually. Any guidance would be very much appreciated.

_{PS: I'm new to posting here, so if I break some sort of rule or violate some sort of expectation, please feel free to enlighten me. I've lurked around a great deal as I've progressed through my first few physics classes, and I have a great deal of respect for everyone here.}

 

[gneill]

Check your conversion for the plate area. How many square centimeters are there in a square meter?

 

[recursive]

Check your conversion for the plate area. How many square centimeters are there in a square meter?

Ah, I see... I was basically only converting one "side" of the square. Guess my intuition was more correct than I gave it credit for.

Thanks--fixing this gave me the correct result. Glad I wasn't misunderstanding the general concept.