Capacitors

A capacitor stores charge on two plates separated by an insulator. It charges and discharges along exponential curves, with the time constant RC setting how fast.

Key facts

  • Q = CV (C in farads).
  • Energy stored E = ½CV² = ½QV.
  • Discharge: Q = Q₀e^(−t/RC).
  • Time constant τ = RC: time to fall to about 37% of the start.

Worked examples

Example 1

A 470 µF capacitor is charged to 12 V. Find the charge and the energy stored.

  1. Q = 470 × 10⁻⁶ × 12 = 5.64 × 10⁻³ C
  2. E = ½ × 470 × 10⁻⁶ × 144 = 0.0338 J

Answer: 5.64 mC and 33.8 mJ