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# Capacitors in DC Circuits

Capacitors are components, in which static electrical charges are stored. In its most basic structure a capacitor consists of two metal plates, which constitute the electrodes of the capacitor. Due to the charge separation an electrical potential difference (voltage) *U* is formed between the electrodes. The subsequent graphic image shows an example of a plate capacitor with plate surface area *A* and plate separation *d*, which carries the charge *Q*. Due to the charge separation an electric field forms between the plates (not shown here).

Normally there is insulating material, a so-called *dielectric*, positioned between the plates (not shown above). There is a linear relationship between the charge and voltage as given by the following expression:

The variable *C* is termed the *capacitance* of the capacitor, which is measured in units called *Farads* (unit symbol: F). The greater the capacitance of a capacitor, the more charge is required to generate a certain voltage between its electrodes. You can take a swimming pool as an analogy for this, whereby the capacitance corresponds to the floor space of the pool, the charge is the amount of water in the pool and the voltage is the level of water. The greater the pool's floor space (capacitance), the more water (charge) you need to put in to achieve a certain water level (voltage).

The capacitance of a capacitor can be considered to be constant. It depends solely on the geometric design and the dielectric material used. For a plate capacitor the following expression is true:

Where e_{0} is the electrical field constant (permittivity of free space) and has a value of 8.8542·10^{-12} AS/Vm, e_{r} is the dielectric constant or relative permittivity (which has no unit), *A* is the surface area of the plate and *d* is the distance between the plates. If a capacitor is connected to a via a charging resistor *R* to a DC voltage *U*_{0}, it charges up to the said voltage, whereby the capacitor voltage increases in accordance with an *e*xponential function from 0 V to its end value *U*_{0} (100%) (charging curve of a capacitor, see graph below, left). If you then disconnect the capacitor from the voltage source and short it out, discharging occurs which is the inverse to the charging process (see graph below, right).

The charging and discharging current characteristics run in opposite directions. Just how fast the capacitor charges up or discharges depends on its capacitance and the value of the series resistance *R* and is characterised by the *time constant* *T* = *R*·*C*. This is the time it takes before the capacitor reaches 63% of its final voltage value when charging or until it has dropped to 63% of its starting voltage when discharging. If the capacitor has charged up completely, no more charging current flows and the capacitor conducts *no DC current at all*.

If after the capacitor has charged up it is disconnected from the voltage source, without any short-circuiting of the circuit, the capacitor retains its charged state and thus in theory retains its voltage indefinitely. In reality, however, there is always a certain amount of intrinsic discharge.

Capacitors come in all sorts of designs for the most varied of applications. Metal-paper capacitors, electrolyte capacitors, tantalum capacitors, plastic film capacitors and small ceramic capacitors are some of the most popular and important designs. |