Capacitors in series and parallel Cambridge International AS & A Level Physics revision
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In plain words
Join capacitors side by side and they act like one bigger capacitor. Join them end to end and, oddly, the pair holds less than either one alone. The rules are the mirror image of the rules for resistors.
4 things to know
- In parallel the p.d. is the same across each capacitor and the charges add up: C = C₁ + C₂ + ...
- In series each capacitor holds the same charge and the p.d.s add up: 1/C = 1/C₁ + 1/C₂ + ...
- Both come from C = Q ÷ V. In parallel, Q = Q₁ + Q₂ = C₁V + C₂V. In series, V = V₁ + V₂ = Q/C₁ + Q/C₂.
- An isolated conducting sphere has a capacitance too: its charge divided by its potential. For a sphere of radius R, C = 4πε₀R.
Worked example
Capacitors of 2.0 µF and 3.0 µF are connected in series across a 10 V supply. Find the combined capacitance, the charge on each and the p.d. across each.
- 1/C = 1/2.0 + 1/3.0 = 5/6, so C = 1.2 µF.
- Charge on each = CV = 1.2 µF × 10 V = 12 µC.
- P.d.s: 12 ÷ 2.0 = 6.0 V and 12 ÷ 3.0 = 4.0 V, which add up to 10 V.
Tips and tricks
- The rules are the opposite way round from resistors: capacitors add up in parallel.
- In series, the smaller capacitor takes the bigger share of the p.d.
It lands in your notebook with its questions as flashcards.
Capacitors in series and parallel: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the combined capacitance of two 10 µF capacitors in parallel?
In parallel, capacitances add.
What is the combined capacitance of two 10 µF capacitors in series?
1/C = 1/10 + 1/10.
What is the same for two capacitors connected in series?
The same charge flows on to each.
What is the same for two capacitors connected in parallel?
They are connected between the same two points.
What is the combined capacitance of three 6 µF capacitors in series?
1/C = 3 × 1/6.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
Capacitors in series and parallel
Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org
Name ______________________________ Date ______________
Find the combined capacitance of 4.0 µF and 6.0 µF in parallel.[2]
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10 µF.
Find the combined capacitance of 6.0 µF and 3.0 µF in series.[2]
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2.0 µF.
Show that two capacitors in parallel have a combined capacitance C = C₁ + C₂.[3]
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The p.d. V is the same across both. The total charge stored is Q = Q₁ + Q₂ = C₁V + C₂V. The combined capacitance is Q ÷ V = C₁ + C₂.
Find the capacitance of an isolated metal sphere of radius 0.10 m.[2]
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1.1 × 10⁻¹¹ F (11 pF). 4π × 8.85 × 10⁻¹² × 0.10.
Answers: Capacitors in series and parallel
- 1. 10 µF.
- 2. 2.0 µF.
- 3. The p.d. V is the same across both. The total charge stored is Q = Q₁ + Q₂ = C₁V + C₂V. The combined capacitance is Q ÷ V = C₁ + C₂.
- 4. 1.1 × 10⁻¹¹ F (11 pF). 4π × 8.85 × 10⁻¹² × 0.10.