Define capacitance and use C = Q/V
Define capacitance for isolated spherical conductors and parallel-plate capacitors, then connect stored charge with potential difference.
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 19. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use charge, potential difference, current, resistance, graph area, energy and SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What is capacitance in terms of charge and potential difference?
What you will learn
- Define capacitance for isolated conductors and parallel-plate capacitors
- Use C = Q/V
- Interpret capacitance as charge stored per unit potential difference
Capacitance describes charge storage per volt
Capacitance C is the ratio of the charge Q stored by a conductor or capacitor to its potential difference V: C = Q/V. A larger capacitance means more charge is stored for each volt. The unit is the farad, with 1 F = 1 C V⁻¹.
This definition applies to an isolated spherical conductor and to a parallel-plate capacitor. For a capacitor, Q is the magnitude of charge on either plate; the two plates carry equal-magnitude opposite charges. The potential difference is measured between the conductors.
Use consistent charge and voltage units
Rearrange as Q = CV or V = Q/C before substituting. A microfarad is 10⁻⁶ F and a nanocoulomb is 10⁻⁹ C. Keep the definition clear: capacitance is not the stored charge itself and is not measured in coulombs.
If charge is plotted against potential difference for a capacitor with constant C, the graph is a straight line through the origin with gradient C when Q is on the vertical axis and V on the horizontal axis.
Pause and explain
A capacitor has C = 5.0 μF and V = 4.0 V. What charge magnitude is on either plate?
Worked example
A capacitor stores 240 μC when its potential difference is 12 V. Calculate its capacitance.
Show the worked solution
- Use C = Q/V.
- Convert 240 μC to 240 × 10⁻⁶ C.
- Express the answer in farads or microfarads.
Answer C = 240 × 10⁻⁶/12 = 20 × 10⁻⁶ F = 20 μF.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A capacitor has C = 8.0 μF and is connected across 15 V. Calculate its stored charge magnitude.
Give me a hint
Use Q = CV and keep μF paired with volts to obtain μC.
Compare my reasoning
- Q = CV.
- Q = 8.0 μF × 15 V = 120 μC.
- The two plates carry equal-magnitude opposite charges.
Q = 120 μC on either plate in magnitude.
Look for these in your work
- Definition rearranged
- Product calculated
- Plate-charge magnitude stated
A 3.0 μF capacitor stores 45 μC. Find its potential difference.
Give me a hint
Rearrange C = Q/V to V = Q/C.
Compare my reasoning
- V = Q/C.
- V = 45 μC/3.0 μF.
- The micro-units cancel, leaving volts.
V = 15 V.
Look for these in your work
- Equation rearranged
- Charge and capacitance units matched
- Voltage stated
A student says a 10 μF capacitor stores 10 μC. Explain why the information is insufficient.
Give me a hint
Capacitance gives charge per volt, not charge by itself.
Compare my reasoning
- C = Q/V, so Q = CV.
- The potential difference V is needed to find Q.
- At 1 V it would store 10 μC, but at another voltage its charge would differ.
The voltage is missing; 10 μF means 10 μC per volt, not a fixed charge of 10 μC.
Look for these in your work
- Definition used
- Missing quantity identified
- Conditional example stated
Common mistakes
- Using Q = V/C instead of Q = CV
- Leaving microcoulombs unconverted when using farads
- Confusing charge with capacitance
- Using the charge on both plates added together instead of the magnitude on one plate
What can you explain now?
What is capacitance in terms of charge and potential difference?
Compare with the explanation
C = Q/V
Capacitance is charge stored per volt.
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Make it stick
What does a capacitance of 1 farad mean in terms of charge and potential difference?
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