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## The capacitor on DC voltage - an energy store

Here is the circuit diagram for a better understanding:

At DC voltage, the **capacitor** acts as a **charge accumulator**. Essentially, the capacitor consists of two plates, which are electrically separated from each other - either by air or by an insulator (dielectric).

A characteristic value of the capacitor is the **capacitance C**. It describes the capacity of the capacitor to store a certain amount of charge Q on its plates at a certain voltage.

**Q = C * V** or **C = Q / V**

Colloquially expressed: "The larger the capacitor and the higher the voltage, the more charges find room on the capacitor plates".

**Unit:** [C] = Farad F = 1 C / V ("One Farad equals one Colomb per Volt")

Usual sizes:

Millifarad mF = 10^{-3}F

Microfarad µF = 10^{-6}F

Nanofarad nF = 10^{-9}F

Picofarad pF = 10^{-12}F

**How to determine the capacity of a capacitor?**

**Plate distance:** The smaller the plate distance, the more the charges on the opposite plate attract each other and the "more" charges therefore find "space" on the plates.

**Plate area A:** The larger the plate areas, the more loads can be stored on the plate.

**Dielectric:** Electric dipoles of the dielectric align themselves with the charges of the capacitor and "neutralize" them. Thus, more charges find place on the plates of the capacitor.

### Charge- and Discharge Curve

#### Determine the **time to charge** or **discharge** a **capacitor**

As can be seen, the charge and discharge curves of a capacitor have a curvilinear shape, which can be described according to an e-function. Therewith, the capacitor would actually never be fully charged, a thing that of course does not make sense in practice.

In general, a capacitor charges and discharges more slowly the larger its capacity and the larger the resistor R in series. This is the basis for the so-called **Time constant Ƭ** (pronounced "Tau"):

**Ƭ = R * C** in seconds **s**

In practice, you would apply the following rule of thumb: The **capacitor** is **fully charged** or **discharged** after **5 Ƭ**. The capacitor voltage has thus reached 0.99 of the supply voltage.

The level of the applied voltage has no influence on the charging time!

Always charge and discharge capacitors - especially larger ones - via a series resistor!

#### Charge and Discharge Equations

#### Exercise - Charge and Discharge Capacitor

The following parallel circuit is connected to a DC voltage of 100 V. How long does it take until both currents I_{1} and I_{2} are equal?