Operation and function of a capacitor; factors affecting capacitance; capacitor types, colour coding and ratings; capacitors in series and parallel; the RC time constant.
Notes
Capacitance — summary notes
Free
Main ideas
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%.
Key formulas
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)
Solved examples
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.