Capacitors · Grade 12
A capacitor stores charge on two plates separated by an insulator. The more charge it holds per volt, the bigger its capacitance (in farads). Capacitors release energy quickly – in camera flashes, defibrillators and backup power – and charge or discharge through a resistor in a smooth exponential curve set by the time constant RC.
Key facts
- Q = CV (1 F = 1 C/V; usually µF).
- Energy stored: E = ½QV = ½CV² = (Q²)/(2C) (the area under a Q–V graph).
- Time constant τ = RC: after one τ a discharging capacitor has 37% of its charge left.
- Discharge: Q = Q₀e^(−t/(RC)) (also for V and I); half-life t½ = RC ln 2 ≈ 0.69RC.
- Capacitors in parallel add; in series 1/C = 1/(C₁) + 1/(C₂).
- When charging from a battery, half the energy supplied is wasted as heat in the resistance.