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The INCORRECT formula representing the energy stored in a parallel plate capacitor in usual notation is

  • A.\(\frac{1}{2}CV^{2}\)
  • B.\(\frac{1}{2}QV\)
  • C.\(\frac{1}{2C}Q^{2}\)
  • D.\(\frac{1}{2}C^{2}V\)
  • E.\(\frac{1}{2}\epsilon_{0}E^{2}Ad\)

Answer: D

The incorrect formula is \(\frac{1}{2}C^{2}V\).

The energy stored is \(U = \frac{1}{2}QV\). With Q = CV it becomes \(\frac{1}{2}CV^{2}\) and \(\frac{Q^{2}}{2C}\). In terms of the field, the energy density \(\frac{1}{2}\varepsilon_0E^{2}\) times the volume Ad gives \(\frac{1}{2}\varepsilon_0E^{2}Ad\).

\(\frac{1}{2}C^{2}V\) has the wrong dimensions (it equals \(\frac{1}{2}CQ\)), so it cannot be an energy.

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