Capacitance & Capacitors
Operation and function of a capacitor; factors affecting capacitance; capacitor types, colour coding and ratings; capacitors in series and parallel; the RC time constant.
Capacitance, summary notes
- A capacitor stores charge on two plates separated by a dielectric. Capacitance C = Q / V, measured in farads.
- Physical construction: C = ε₀εᵣA / d. Larger plate area or a thinner dielectric gives more capacitance.
- Energy stored is E = ½CV².
- Capacitors in PARALLEL add (C_T = ΣC). In SERIES, 1/C_T = Σ(1/C). This is the exact opposite of resistors.
- Charging through a resistor follows the time constant τ = RC. After 1τ the capacitor reaches 63.2% of the supply; it is regarded as fully charged after 5τ.
- Electrolytic capacitors are polarised and will fail, often violently, if connected the wrong way round.
- ⚠ Exam trap: the series/parallel rule is inverted compared with resistors, and one time constant gives 63%, not 100%.
- Capacitance
- C = Q / V (farads)
- Parallel-plate capacitor
- C = ε₀εᵣA / d
- Energy stored
- E = ½CV²
- Capacitors in parallel
- C_T = C₁ + C₂ + C₃ …
- Capacitors in series
- 1/C_T = 1/C₁ + 1/C₂ + 1/C₃ …
- Time constant
- τ = R × C (63.2% in 1τ)
Three 6 µF capacitors are connected in series. Find the total capacitance.
1/C_T = 1/6 + 1/6 + 1/6 = 3/6, so C_T = 2 µF. Series capacitance is smaller than the smallest capacitor.
A 100 µF capacitor charges through a 10 kΩ resistor. How long is one time constant, and what voltage is reached from a 20 V supply?
τ = RC = 10 000 × 100 × 10⁻⁶ = 1 s. After 1τ the capacitor reaches 63.2% of 20 V = 12.6 V.
RC charging & the time constant
Capacitance concept map
Capacitance
Capacitance quiz
Capacitance & Capacitors, quiz
1. A 4 microfarad and a 12 microfarad capacitor in series give a total of:
3 microfarads16 microfarads48 microfarads2. The two capacitors shown are in series. The total capacitance is:
2 µF9 µF4.5 µF3. The two capacitors shown are in parallel. The total capacitance is:
9 µF2 µF18 µF4. In the circuit shown the switch is closed. The time constant of the circuit is:
1 second0.1 second10 seconds5. Three 6 µF capacitors are connected in series. The total capacitance is:
2 µF9 µF18 µF6. After one time constant, a charging capacitor reaches what percentage of the supply voltage?
63 %37 %100 %7. Three 6 µF capacitors in parallel give a total of:
18 µF2 µF6 µF8. The energy stored in a capacitor is given by:
E = ½CV²E = ½LI²E = CV9. Increasing the distance between capacitor plates:
Decreases capacitanceIncreases capacitanceHas no effect10. A 100 µF capacitor charges through a 10 kΩ resistor. One time constant is:
1 second0.1 second10 seconds11. A capacitor is regarded as fully charged after approximately:
5 time constants1 time constant2 time constants12. Which type of capacitor is polarised?
ElectrolyticCeramicMica