OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(b) energy stored by capacitor; W = 1/2 QV, W = 1/2 CV² and W = 1/2 Q²/C
Full specification wording
Energy: (b) energy stored by capacitor; W = 1/2 QV, W = 1/2 CV² and W = 1/2 Q²/C
The energy stored by a capacitor can be written in three equivalent forms using Q = CV.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 2 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The energy stored by a capacitor can be written in three equivalent forms using Q = CV. Starting from W = ½QV, substituting Q = CV gives W = ½CV², and substituting V = Q/C gives W = ½Q²/C. Each form is useful depending on which quantities are known.
For example: A 2.0 × 10⁻⁶ F capacitor charged to 12 V stores W = ½ × 2.0 × 10⁻⁶ × 12² = 1.44 × 10⁻⁴ J. The factor ½ arises because the p.d. rises from zero to V as charge is transferred, so the average p.d. during charging is ½V. Choosing the right form avoids unnecessary intermediate calculations.
What earns the marks
- State the three equivalent expressions W = ½QV, W = ½CV² and W = ½Q²/C for energy stored by a capacitor.
- Derive the alternative forms from W = ½QV using Q = CV.
- Select the most convenient form based on the quantities given in a problem.
- Calculate energy stored correctly, keeping charge in coulombs, p.d. in volts and capacitance in farads.
Common mistakes and how to put them right
Omitting the factor ½ and using W = QV or W = CV².
Put it right: The correct expressions all include ½.
Mixing units, such as using capacitance in microfarads without converting to farads, which gives an energy a million times too large.
Substituting the wrong rearrangement, for example using V = Q/C when Q is unknown.
Put it right: Choose the form matching the given data.
Exam tips
- Write down the known quantities with units first, then choose the form of the energy equation that uses them directly.
- Convert microfarads to farads (× 10⁻⁶) and nanocoulombs to coulombs (× 10⁻⁹) before substituting.
- Check the answer is in joules and is reasonable for the size of capacitor and p.d. given.
Try the lesson
The start of the Energy: (b) energy stored by capacitor; W = 1/2 QV, W = 1/2 CV² and W = 1/2 Q²/C lesson, made from checked teaching notes for this specification point.
Listen
The energy stored by a capacitor can be written in three equivalent forms using Q = CV. Starting from W = ½QV, substituting Q = CV gives W = ½CV², and substituting V = Q/C gives W = ½Q²/C. Each form is useful depending on which quantities are known. For example, a 2.0 × 10⁻⁶ F capacitor charged to 12 V stores W = ½ × 2.0 × 10⁻⁶ × 12² = 1.44 × 10⁻⁴ J. The factor ½ arises because the p.d. rises from zero to V as charge is transferred, so the average p.d. during charging is ½V. Choosing the right form avoids unnecessary intermediate calculations. A strong answer earns marks for these points. State the three equivalent expressions W = ½QV, W = ½CV² and W = ½Q²/C for energy stored by a capacitor. Derive the alternative forms from W = ½QV using Q = CV. Select the most convenient form based on the quantities given in a problem. Calculate energy stored correctly, keeping charge in coulombs, p.d. in volts and capacitance in farads. Exam tip: Write down the known quantities with units first, then choose the form of the energy equation that uses them directly.
See it
Key words
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Energy storage in a capacitor
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Equivalent energy formulae
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Use of Q = CV to transform expressions
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Selection of appropriate equation
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See every definition
- Energy storage in a capacitor
- The energy stored by a capacitor can be written in three equivalent forms using Q = CV.
- Equivalent energy formulae
- W = ½QV, W = ½CV² and W = ½Q²/C are the three equivalent expressions for energy stored by a capacitor.
- Use of Q = CV to transform expressions
- Substituting Q = CV into W = ½QV gives W = ½CV², and substituting V = Q/C gives W = ½Q²/C.
- Selection of appropriate equation
- Each form is useful depending on which quantities are known, and choosing the right form avoids unnecessary intermediate calculations.
Label the diagram
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