CIE A Level Physics

Revision Notes

A LevelPhysicsCIERevision Notes19. Capacitance19.1 Capacitors19.1.5 Energy Stored in a Capacitor

Syllabus Edition

First teaching 2020

Last exams 2024

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19.1.5 Energy Stored in a Capacitor

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Calculating Energy Stored in a Capacitor

  • Recall the electric potential energy is the area under a potential-charge graph
  • This is equal to the work done in charging the capacitor to a particular potential difference
    • The shape of this area is a right angled triangle

  • Therefore the work done, or energy stored in a capacitor is defined by the equation:

W space equals space 1 half Q V

  • Substituting the charge with the capacitance equation Q = CV, the work done can also be defined as:

W space equals space 1 half C V squared

  • Where:
    • W = work done/energy stored (J)
    • Q = charge on the capacitor (C)
    • V = potential difference (V)
    • C = capacitance (F)

  • By substituting the potential V, the work done can also be defined in terms of just the charge and the capacitance:

W space equals space fraction numerator Q squared over denominator 2 C end fraction

Worked example

Calculate the change in the energy stored in a capacitor of capacitance 1500 μF when the potential difference across the capacitor changes from 10 V to 30 V.

Step 1: Write down the equation for energy stored in terms of capacitance C and p.d V

W space equals space 1 half C V squared

Step 2: The change in energy stored is proportional to the change in p.d

increment W space equals space 1 half C V subscript 2 squared space minus space 1 half C V subscript 1 squared space equals space 1 half C open parentheses V subscript 2 squared space minus space V subscript 1 squared close parentheses

Step 3: Substitute in values

increment W space equals space 1 half space cross times space open parentheses 1500 cross times 10 to the power of negative 6 end exponent close parentheses space cross times space left parenthesis 30 squared space minus space 10 squared right parenthesis

increment W space equals space 0.6 space straight J

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