Capacitors

Capacitors store energy in the electrostatic field of charge ($Q[C]$) on conductive plates separated by a distance.

Applying a voltage, $V_c(t)$ forces a proportional charge imbalance of $Q$. This is analogous to storing energy in a stretched spring or placing a stretchy balloon membrane in a pipe.

This proportionality is called the capacitance ($C[F]$) and states how much charge, $Q$, is pushed onto the capacitor for a given voltage, $V$:

$$Q=CV$$

Taking the time derivative of both sides gives an $I-V$ relationship:

$$I=C\frac{dV}{dt}$$

A bigger capacitor can store more $Q$ for a given $V$.

• Analogy: A bike tire has more less air ($Q$) for a given pressure ($V$) versus a bouncy castle, which has significantly more air; so, the bike tire has less capacitance than the bouncy castle.