A capacitor is a device that stores electric charge and energy. It is two conductors separated by an insulator; when connected to a battery they acquire equal and opposite charges $\pm Q$. The capacitance measures how much charge the device holds per unit potential difference:
$$C=\frac{Q}{V}$$ The SI unit is the farad (F = C/V). A farad is very large, so practical values are in $\mu\text{F}$, $\text{nF}$ and $\text{pF}$. Capacitance depends only on the geometry of the conductors and the medium between them — not on the charge or voltage applied.
For a parallel-plate capacitor of plate area $A$ and separation $d$ with vacuum between the plates,
$$C=\frac{\epsilon_0 A}{d}$$ Larger plates and a smaller gap give a larger capacitance. The uniform field between the plates is $E=\frac{\sigma}{\epsilon_0}=\frac{V}{d}$.
Capacitors are combined in two ways:
- Series: the same charge sits on each capacitor and voltages add, so $\frac{1}{C_s}=\frac{1}{C_1}+\frac{1}{C_2}+\dots$ — the net capacitance is less than the smallest member.
- Parallel: the voltage is common and charges add, so $C_p=C_1+C_2+\dots$ — the net capacitance is the sum.
Inserting a dielectric (an insulator such as glass, mica or oil) of dielectric constant $K$ multiplies the capacitance: $C=K\frac{\epsilon_0 A}{d}=KC_0$. The dielectric reduces the effective field because its molecules polarise and set up an opposing field, allowing the capacitor to store more charge at the same voltage. This is why real capacitors are filled with dielectric.
The energy stored in a charged capacitor, equal to the work done to charge it, is
$$U=\frac12 CV^2=\frac12 QV=\frac{Q^2}{2C}$$ This energy resides in the electric field between the plates; the energy density (energy per unit volume) is $u=\frac12\epsilon_0 E^2$. Capacitors are everywhere — in power supplies, camera flashes, defibrillators and tuning circuits — wherever rapid storage and release of energy is needed.