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Energy Stored by a Capacitor

Physics: AQA A Level, topic 7.4.3

Energy of a Capacitor - QV Graphs

The work done on a charge (Q) in moving through a potential difference of ΔV is equal to QΔV. This helps to find the energy stored by a capacitor.

Transporting charge

Transporting charge

  • Imagine a parallel plate capacitor that has a potential difference of V. The definition of capacitance says that Q = CV.
  • By transporting a tiny amount of charge, ΔQ, from the negative plate to the positive plate, the potential difference is approximately constant.
Area under graph

Area under graph

  • The increase in energy stored is equal to the energy gained by the charge, i.e. VΔQ. This is equal to the area shaded on the graph.
  • This means that the total energy stored will equal the area of the triangle: ½QV.

Capacitor Equations

Capacitors are easy to handle if you know what equation to use.

Capacitance

Capacitance

  • Definition of capacitance:
  • C=QVC=\frac{Q}{V}
  • Capacitance of a parallel plate:
  • C=Aϵ0ϵr/dC=A{{\epsilon}_0}{{\epsilon}_r}/d
Energy

Energy

  • The energy stored in a capacitor is:
  • E=12QVE=\frac{1}{2}QV
  • By using the definition of capacitance, you can rearrange to get:
  • E=12CV2E=\frac{1}{2}CV^2
  • E=12Q2CE=\frac{1}{2}\frac{Q^2}{C}

Test yourself on Energy Stored by a Capacitor

  • What is the definition of capacitance?

  • What is the correct equation for the energy stored in a capacitor?

  • What is the equation of the capacitance of a parallel plate capacitor?

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