A LevelPhysicsCIERevision Notes19. Capacitance19.2 Energy Stored in a CapacitorEnergy Stored in a Capacitor

Syllabus Edition

First teaching 2023

First exams 2025

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Energy Stored in a Capacitor (CIE A Level Physics)

Revision Note

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Ann H

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Ann H

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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.

Answer:

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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    Ann H

    Author: Ann H

    Ann obtained her Maths and Physics degree from the University of Bath before completing her PGCE in Science and Maths teaching. She spent ten years teaching Maths and Physics to wonderful students from all around the world whilst living in China, Ethiopia and Nepal. Now based in beautiful Devon she is thrilled to be creating awesome Physics resources to make Physics more accessible and understandable for all students no matter their schooling or background.