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Consider a parallel plate capacitor with metal plates, each of square shape of 1.00 m on a side, separated by 1.00 mm. If the plates grow in area while the voltage is held fixed, the capacitance ___ and the stored energy ___.
  1. decreases, decreases
  2. decreases, increases
  3. increases, decreases
  4. increases, increases
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OpenStax College Physics for AP® Courses Solution, Chapter 19, Problem 43 (Test Prep for AP® Courses) (0:54)

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This is College Physics Answers with Shaun Dychko. We need to make expressions for both capacitance and energy in terms of area. So, the energy is going to be capacitance times voltage squared over two, but to make sense of that, we need to substitute for this capacitance with this expression, which is permittivity of free space times the area of the plates divided by the separation between them. So, we can see that as the area increases, the capacitance will increase because capacitance is directly proportional to area. So, that narrows our possibilities down to C or D. And then, the energy, when we substitute this in place of C, we can see that the energy also is directly proportional to the area, and so the energy increases also as the area increases. And so, the answer is D.