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# December 2017

## Rectangular Alternating Voltage for a Capacitor

To investigate the behaviour of a capacitor in an AC circuit, let us first work through a theoretical scenario. As shown in the left-hand part of the diagram below, a capacitor is connectable via a switch S and a resistor *R* to one of two direct voltage sources (e.g. batteries) of different polarities. Varying the switch position then supplies the RC network with a periodically changing rectangular alternating voltage.

## Charging and Discharging of Capacitors

The processes of charging and discharging a capacitor are already familiar from the treatment of *DC circuits*: Connecting a capacitor via a charging resistor *R* to a direct voltage *U*_{0} causes the capacitor to be charged to this voltage. The potential rises exponentially from 0 V to the final value of *U*_{0}.

## Series and Parallel Connection of Capacitors

**Parallel Connection of Capacitors:**

The diagram below shows an example of capacitors connected in parallel. In this case, the same voltage *U* is present across all capacitors.

## Capacitance and Capacitors

Capacitance and capacitors Capacitors are components which store static electric charge. A capacitor essentially consists of two metal plates serving as electrodes. Charge separation leads to an electric potential difference (voltage) U between the electrodes. The diagram below shows an example of a plate capacitor with a plate area A and plate spacing d carrying a charge Q. The charge separation produces an electric field (not shown here) between the plates.

## Addition of Alternating Quantities

If two sinusoidal alternating quantities like the voltages u1 and u2 considered on the previous page need to be added, their instantaneous values at any point in a line diagram are added algebraically (refer to the right-hand side of the diagram below). A total voltage u is thus obtained. A line diagram also permits alternating quantities of different frequencies to be added in this manner.

## Vector Diagrams

The time characteristic of sinusoidal alternating voltages and currents can be represented not only by means of the line diagrams we have seen so far, but also by vector diagrams which can prove more appropriate in certain cases. The illustrations below show the relationship between the line and vector diagrams of a sinusoidal alternating voltage *u* with a peak value *u*_{0} and frequency *f*.

## Applications and Advantages of Alternating Quantities

Alternating current and three-phase current (a special form of alternating current) nowadays dominate most areas of electrical engineering, including energy technology, communications engineering and information technology. This is due, in particular, to the following advantages:

## Root-Mean-Square Value of Voltage and Current

Applying a sinusoidal voltage u(t) to a resistive load R causes the following current to flow through the load according to Ohm's law:

## Characteristic Parameters of Sinusoidal Signals

The instantaneous value *u*(*t*) of a sinusoidal alternating voltage is given by the equation.

## DC and AC Voltages

by friction between two materials was one source of DC voltage. Early machines generating (very low levels of) electric power such as electrostatic machines, inductance machines and belt generators as well as the batteries developed during this period produced DC voltages as well, i.e. they gave rise to direct current when resistive loads were connected. Today, DC voltages are mainly used to supply electronic circuits, e.g. in radios, pocket calculators and PCs. |

## ALTERNATING CURRENT CIRCUITS TRAINING

This course imparts the fundamentals of AC circuits. Main subjects include calculations of AC variables and basic electrical properties of AC circuits such as *resistance*, *capacitance*and *inductance*. Special consideration is paid here to filter (high-pass and low-pass) circuits as well as resonant circuits. The course is completed by a treatment of the fundamentals of transformers.

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