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The Energy Stored In Capacitors


The capacitance is the amount of charge stored per volt of potential difference. Due to the equation C = Q/V, the capacitance is measured in coulombs per volt (C/V).  1 coulomb/volt = 1 Farad.
This brings us onto the equation for capacitance:
Q = CV
Where...
  • Charge (Q) is measured in coulombs.
  • Capacitance (C) is measured in Farads.
  • Voltage (V) is measured in volts.
On a graph of of Q = CV, the gradient of the graph is the capacitance with the area under the graph being the energy transferred (work done).

Energy Stored in a Capacitor using the graph Q = CV (y = mx) 
  • Area of triangle = work done
  • =1/2 x base x height
  • Work done = 1/2 QV. But, Q = CV.
Therefore, W = 1/2 CV^2 where:
  • Work done is energy measured in joules. 
  • Capacitance in Farads and voltage in volts.

Example

A typical capacitor is 100 micro-Farads. It is charged to 5 volts. What charge is stored by the above pair of values?
  • Q = CV = 100x10-6 x 5
  • Charge = 5x10-4 Coulombs
What energy is stored?
  • Work Done or Energy E = 1/2 x CV^2
  • E = 1/2 x 100x10^-6 x 5^2.
  • E = 1.25x10^-3 Joules.

Summary

  • The charge of a capacitor can be worked out using the equation Charge (Q) = Capacitance (Farads) x Voltage (V).
  • The graph of Q against V produces the gradient as the capacitance.
  • The area under the graph is the work done or energy. This produces the equation E = 1/2 x CV^2.

About Will Green

A student in England studying Automotive Engineering with Motorsport, Will created Ask Will Online back in 2010 to help students revise and bloggers make money. You can follow AskWillOnline via @AskWillOnline.

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