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close this bookIntroduction to Electrical Engineering - Basic vocational knowledge (Institut für Berufliche Entwicklung, 213 p.)
View the document(introduction...)
View the documentPreface
View the document1. Importance of Electrical Engineering
close this folder2. Fundamental Quantities of Electrical Engineering
View the document2.1. Current
View the document2.2. Voltage
View the document2.3. Resistance and Conductance
close this folder3. Electric Circuits
View the document3.1. Basic Circuit
View the document3.2. Ohm’s Law
close this folder3.3. Branched and Unbranched Circuits
View the document3.3.1. Branched Circuits
View the document3.3.2. Unbranched Circuits
View the document3.3.3. Meshed Circuits
close this folder4. Electrical Energy
View the document4.1. Energy and Power
View the document4.2. Efficiency
View the document4.3. Conversion of Electrical Energy into Heat
View the document4.4. Conversion of Electrical Energy into Mechanical Energy
close this folder4.5. Conversion of Electrical Energy into Light
View the document4.5.1. Fundamentals of Illumination Engineering
View the document4.5.2. Light Sources
View the document4.5.3. Illuminating Engineering
View the document4.6. Conversion of Electrical Energy into Chemical Energy and Chemical Energy into Electrical Energy
close this folder5. Magnetic Field
View the document5.1. Magnetic Phenomena
View the document5.2. Force Actions in a Magnetic Field
close this folder5.3. Electromagnetic Induction
View the document5.3.1. The General Law of Induction
View the document5.3.2. Utilisation of the Phenomena of Induction
View the document5.3.3. Inductance
close this folder6. Electrical Field
View the document6.1. Electrical Phenomena in Non-conductors
close this folder6.2. Capacity
View the document6.2.1. Capacity and Capacitor
View the document6.2.2. Behaviour of a Capacitor in a Direct Current Circuit
View the document6.2.3. Types of Capacitors
close this folder7. Alternating Current
View the document7.1. Importance and Advantages of Alternating Current
View the document7.2. Characteristics of Alternating Current
View the document7.3. Resistances in an Alternating Current Circuit
View the document7.4. Power of Alternating Current
close this folder8. Three-phase Current
View the document8.1. Generation of Three-phase Current
View the document8.2. The Rotating Field
View the document8.3. Interlinking of the Three-phase Current
View the document8.4. Power of Three-phase Current
close this folder9. Protective Measures in Electrical Installations
View the document9.1. Danger to Man by Electric Shock
close this folder9.2. Measures for the Protection of Man from Electric Shock
View the document9.2.1. Protective Insulation
View the document9.2.2. Extra-low Protective Voltage
View the document9.2.3. Protective Isolation
View the document9.2.4. Protective Wire System
View the document9.2.5. Protective Earthing
View the document9.2.6. Connection to the Neutral
View the document9.2.7. Fault-current Protection
View the document9.3. Checking the Protective Measures

2.2. Voltage

In order that a current flows through a conductor, an electrical “pressure” must be exerted on the freely mobile charge carriers. This “pressure” is the electrical drive phenomenon on the charge carriers which is called voltage. There is no current without an electrical voltage.

The original drive phenomenon for current is called primary electromotive force. It is generated in a voltage source. It imparts energy to the charge carriers which thus are driven through the conductor.

Since every conductor offers resistance more or less to the passage of current, the charge carriers lose energy when passing through. This loss can be characterised as voltage drop.

A current can only flow through a conductor; therefore, the current path formed by the conductor must be closed.

When a charge carrier has received drive energy from a voltage source, it passes through the conductor, completely transferring the energy taken up to this conductor. After exactly one circulation, the charge carrier differs by nothing from its state bevor it started the circulation, that is to say, it cannot have stored energy.

The primary electromotive force is designated by the formula sign E, the voltage drop by U. In practice, no difference is made between these two terms and they are called voltage in short. Primary electromotive force and voltage drop have the same unit which is called volt - V in honour of the Italian physicist Alessandro Volta (1745 - 1827).

[E] = V
[U] = V

Frequently used sub-units of volt are

1 MV = 1 megavolt = 106 V = 1,000,000 V
1 kV = 1 kilovolt = 103 V = 1,000 V
1 mV = 1 millivolt = 10-3 V = 0.001 V
1 µV = 1 microvolt = 10-6 V = 0.000001 V

In electrical engineering, voltages may occur in quite different magnitudes. Table 2.2. shows some values.

Table 2.2. Voltage Values for a Few Applications

Lightning up to

10.000,000 V


10 MV

Extra-high voltage lines

600,000 V


600 kV

High-voltage lines

60,000 V


60 kV

Sparking-plug in an internal combustion engine

15,000 V


15 kV

Lighting network

220 V

Motor-car battery

12 V

Receiving voltage of a wireless set

0.000,01 V


10 µV

The primary electromotive force is a prerequisite for an electrical current. Table 2.5. shows the various possibilities of producing a primary electromotive force, the designations of the respective voltage sources and their main applications.

For the winning of electrical energy, the generation of the primary electromotive force by chemical and magnetic-field actions is of particular importance. On principle, these voltage sources operate as follows

· Primary electromotive force by chemical action

When immersing two conductors of different kinds into an electrolyte, then one will find an excess of electrons at one conductor (negative pole) and an electron deficit at the other conductor (positive pole). This charge carrier difference externally acts as electrical primary electromotive force. Diluted sulphuric acid H2SO4 is suitable as electrolyte; as conductor rods (electrodes), copper Cu and zinc Zn are particulary suitable (Fig. 2.6.).

Table 2.3. Ways of Producing Primary Electromotive Forces

Causes of the production of the electromotive force

Designation of the voltage source

Examples of use

chemical action

galvanic cell; battery; accumulator

voltage supply to portable devices; starting battery in motor-cars

thermal action

thermoelectric element (thermocouple)

measuring the temperature at points which are not readily accessible; remote temperature measurement

action of magnetic field (induction)


economical generation of electrical energy in power stations

action of light

photovoltaic cell; solar cell

measuring the intensity of illumination

charge separation by

- influence

influence machine

generation of high and extra-high voltages by means of which, for example, the properties of insulating materials are tested

- mechanical charge movement

belt-type generator

displacement of charge (polarisation) on a non-conductor by means of pressure

piezoelectric element

measurement of pressure; sound pick-up for records; microphone

Fig. 2.6. Galvanic element also known as galvanic cell

Other substances are also suitable (especially coal and zinc in a thickened ammonium chloride solution).

In accordance with the general tendency to balance differences in concentration, the basic units of construction of the solid conductors are eager to migrate as ions in the electrolyte. On the other hand, the electrolyte tries to press its ions into the solid conductor. This impetus of motion is different in the different conductor materials so that, as a result, a primary electromotive force acts externally.

When current flows, these voltage sources disintegrate due to the transport of substance and become useless; this is also occurring when stored too long. Rechargeable voltages sources do not show this disadvantage, therefore, they are called accumulators (storage batteries). Lead accumulators and nickel-iron or nickel-cadmium accumulators are of particular importance.

· Primary electromotive force by magnetic-field action (induction)

This production of voltage is of greatest technical importance and it is used in all cases when primary electromotive force is to be generated by mechanical motion. According to a law of nature (law of induction) the following happens:

When the magnetic flux enclosed by a conductor loop is changed, the charge carriers in the conductor are subjected to an impetus to move. Then, the entire conductor loop is a primary electromotive force source.

The change of the magnetic flux may, for example, be due to the fact that the conductor loop is turned inside the magnetic field or the magnet is approached to are moved away from this loop.

Fig. 2.7. Primary electromotive force 2 generated by induction

1 - Direction of motion
2 - Direction of the primary electromotive force
3 - North pole
4 - South pole

As symbol of a voltage source, the graphical symbol shown in Fig. 2.8. is used. The electrode with an excess of electrons is called negative pole (-); the electrode with an electron deficit is called positive pole (+).

Fig. 2.8. Graphical symbol of a (direct) voltage source; the arrow indicating the direction may be omitted

The direction of voltage corresponds to the direction of current defined in Section 2.1.; thus, the primary electromotive force E is directed from - to + whereas the voltage drop U runs from + to -.

The voltage direction is indicated by an arrow.

The electrical drive exerted on the charge carriers is called voltage. The drive phenomenon originally generated in a voltage source is called primary electromotive force E; the loss in voltage caused when current flows through a conductor is called voltage drop U. As unit of the voltage, the volt - V - has been laid down; the most frequently used sub-units are MV, kV and µV. For the winning of electrical energy, the generation of the primary electromotive force by chemical action and by the action of the magnetic field is of particular importance.

Questions and problems:

1. How many V are

500 mV; 2,5 kV; 350 µV; 0,6 MV?

2. Give reasons for the fact why in a current passage the sum of all voltage drops must be equal to the entire primary electromotive force!