A capacitor stores energy in an electric field between two conductive plates. Unlike a resistor, it does not dissipate energy — it holds charge and gives it back. That storage is what makes timing, filtering and smoothing circuits possible.
Charge, voltage and capacitance
The charge stored on a capacitor is proportional to the voltage across it. The constant is the capacitance, measured in farads (F):
Q = C × V
A farad is a large unit; real capacitors are usually microfarads (µF, 10⁻⁶), nanofarads (nF, 10⁻⁹) or picofarads (pF, 10⁻¹²). The energy stored is:
E = ½ × C × V²
Current and voltage are linked by rate of change
A capacitor's current depends not on the voltage across it but on how fast that voltage is changing:
I = C × (dV/dt)
Two consequences fall straight out of this. The voltage across a capacitor cannot change instantly (that would demand infinite current). And in steady-state DC, once the voltage has settled, dV/dt is zero, so no current flows — a fully charged capacitor behaves like an open circuit.
The RC time constant
Charge a capacitor through a resistor from a supply Vs and the voltage rises along an exponential curve:
Vc(t) = Vs × (1 − e^(−t / RC))
The product RC has units of seconds and is called the time constant, written τ (tau):
τ = R × C
With R = 10 kΩ and C = 10 µF, τ = 10,000 × 0.00001 = 0.1 s = 100 ms. The time constant is the natural clock of the circuit:
- After 1τ the capacitor reaches about 63% of the supply voltage.
- After 2τ, about 86%; after 3τ, about 95%.
- After 5τ it is about 99.3% charged — close enough that engineers treat it as fully charged.
For our 5 V example with τ = 100 ms, that means about 3.16 V after 100 ms and about 4.97 V after 500 ms. Discharging follows the mirror-image curve, Vc(t) = V0 × e^(−t/RC), falling to 37% of its start after one τ.