Capacitance and Capacitors
What a capacitor does
Two conductors separated by a dielectric store charge: C = Q/V, measured in farads (F). For a parallel-plate capacitor, C = ε₀ε_r A/d - larger area or higher permittivity raises capacitance, greater separation lowers it. Capacitance is a property of construction, not of applied voltage. Working voltage and dielectric strength limit the voltage that may be applied; exceeding it causes breakdown.
Energy stored: W = ½CV². A capacitor retains this energy after the supply is removed, hence bleed resistors and discharge procedures.
Series and parallel
Parallel capacitors add: C = C₁ + C₂ + .... Series capacitors combine like parallel resistors: 1/C = 1/C₁ + 1/C₂, giving a total smaller than the smallest. Voltage divides across series capacitors in inverse proportion to capacitance.
Transients
Charging follows an exponential with time constant τ = RC (seconds for ohms x farads). After one τ the capacitor reaches 63% of its final voltage; after five τ it is effectively charged. Current is greatest at switch-on and decays to zero.
Types and traps
Ceramic, film and mica types are stable and non-polarised. Aluminium electrolytic and tantalum capacitors are polarised - reverse connection destroys them - and have significant leakage and wide tolerance. A capacitor blocks DC and passes AC; capacitive reactance falls as frequency rises.
Traps
- Series capacitors give a total smaller than the smallest - the reverse of resistors.
- Capacitor current depends on the rate of change of voltage, not on voltage itself.
- A capacitor looks like an open circuit only once charged.
Worked example
10 µF and 10 µF in series = 5 µF. With 1 MΩ, τ = 5 µF x 1 MΩ = 5 s.