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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

2.1. Current

Flowing quantities of electricity cause effects which are utilised in practice, i.e. in electrical engineering. Since flowing quantities of air are called an air current, flowing quantities of water a water current, the phenomenon of flowing quantities of electricity is called electrical current.

The carriers of the quantities of electricity are called charge carriers. Mostly the latter are electrons, in rare cases ions. An electron has the smallest imaginable charge which, therefore, is called elementary charge. In electro-technology, electrons are considered as practically massless charge carriers because of their small volume and extremely small mass.

Electrons are constituents of atoms, the basic units of which the material world is constructed. An atom consists of a nucleus and the electrons surrounding it. Atoms or groups of atoms which have lost or gained one or more electrons are called ions. Ions are charge carriers having mass. When an ion - as compared with the chargelss neutral atom - has more electrons, then it is called negatively charged, when it has less electrons, it is called positively charged. The electron itself has a negative charge.

As a current consists of flowing quantities of electricity (charge quantities), it can only flow in such substances which possess freely mobile, non-stationary charge carriers. Substances with many mobile charge carriers are called conductors. They include all metals (especially silver, copper, aluminium and iron) and electrolytes (salt solutions). As the current in metals is carried by electrons, it is called electron current, whereas the current flowing through electrolytes is called ion current because the flowing charge carriers are ions.

Fig. 2.1. Electron current; the free electrons move through the atomic lattice of the conductor

1 - Atomic union
2 - Conductor electrons

Fig. 2.2. Ion current

1 - Metallic feed lines
2 - Electrolyte
3 - Electrons
4 - Negative ions
5 - Positive ions
6 - Neutral molecules

Substances in which the charge carriers are fixed or stationary, that is to say, they are not freely mobile, are called non-conductors or insulators. Current cannot flow through them. The most important non-conductors are procelain, glass, plastics.

There are substances whose electrical conductivity is such that they are between conductor and non-conductor. They conduct current so badly that they cannot be termed as conductor but they allow a small current to flow so that they cannot be used as a non-conductor. These substances are called semiconductor. The most important semiconductors are silicon, germanium and selenium. Semiconductors are of particular practical importance to electrical engineering.

We cannot perceive electrical currents directly but only indirectly we become aware of three characteristic effects of current.

These are

1. the generation of heat in conductors through which current flows
2. the magnetic field associated with the current
3. transport of substance by ion currents

Re 1. - Every electric current generates electric heat in conductors. It is utilised in electric heating engineering, for example, cooking plate, flat iron. The generation of electric heat can be imagined in such a way that the flowing charge carriers collide with the stationary particles forming the skeleton of the material or substance. As a consequence, the energy of the braked charge carriers is converted into irregular oscillatory energy, namely thermal energy, of the stationary particles.

Fig. 2.3. Development of heat in the current carrying conductor

Re 2. - Every electric current is accompanied by a magnetic field. It surrounds the current spatially like an eddying fluid its axis of eddy. There is no current without a magnetic eddy and no magnetic field eddy without current. Proof of this can easily be given by means of a magnetic needle which with initial direction parallel to the current will be turned so that it is across to the current. The mutual coupling of current and magnetic field is of eminent practical importance, for example, for an economic production of electrical energy (see Section 5).

Fig. 2.4. Magnetic field associated with the current

1 - North pole
2 - South pole

Re 3. - When a fluid conductor with ions is interposed in a metallic current path, material changes will take place at the two feed wires when current flows. These material changes are the result of the material particles flowing with the ions, in other words, a consequence of the transport of substance associated with the current. From the ions, the electrons can migrate into the current supply leads or out of them; this cannot be effected by the material particles which, consequently, are deposited at these leads. If, for example, the fluid conductor is a copper sulphate solution, the copper particles are separated at one electrode in the form of a metallic coat. This process is called electrolysis. It is used for the winning of metals, especially metals in a pure state, for the deposition of metallic coats and protective coverings (galvanisation).

Fig. 2.5. Transport of matter in case of conduction by ions

In order to define the intensity of a current, the term current intensity (formula sign I) has been introduced.

Obviously, it is independent of the place of the line, the line material and the line cross-sectional area but it is only determined by the number of charge carriers (quantity of charge Q) flowing through the line in a certain time t. When, in a certain time, many charge carriers flow through the conductor, then the current intensity is high, vice versa it is low.

The following holds:



I = Q/t


current intensity


charge quantity



The sign of the current intensity indicates the current direction. It is an arbitrarily established mathematical direction of counting and should not be confused with the aktual flowing direction of the moved charge carriers. One has defined:

The current intensity is positive when the current direction is equal to the direction of flow of the positive charge carriers or when it is opposite to the direction of flow of negative carriers (e.g. electrons).

The unit of current intensity is called ampere = A in honour of the French physicist Marie Andrmp (1775 - 1836).

[I] = A

Other usually used units of the ampere are

1 kA = 1 kiloampere = 103 A = 1.000 A
1 mA = 1 milliampere = 10-3 A = 0.001 A
1 µA = 1 microampere = 10-6 A = 0.000001 A

In electrical engineering, current intensities may occur in largely different magnitudes. Table 2.1. shows a few values.

Table 2.1. Current Intensities for a Few Applications

Melting furnace

100,000 A


100 kA

Aluminium production

10,000 A


10 kA


1,000 A


1 kA

Starter for motor-car

100 A

Household appliances up to

6 A


0,5 A


500 mA

Torch lamp

0,2 A


200 mA

After the establishment of the basic unit for the current intensity, units for the quantity of electricity can be derived from equation (2.1.), namely

Q = I · t
[Q] = [I] · [t]
[Q] = A · s and from 1A · 1s = 1C = 1 coulomb follows
[Q] = C

The product of A · s is called coulomb in honour of the French physicist Charles Auguste de Coulomb (1736 - 1806).

A larger unit of the quantity of electricity is the ampere-hour (a.h). As 1 hour has 3,600 seconds, the following relation holds for the conversion of A.s into A.h:

1 A · h = 1 A · 3600 s = 3600 A · s = 3600 C

The electrical current is the phenomenon of flowing quantities of electricity. The carriers of the quantities of electricity are called charge carriers; these are electrons and ions. As to their conductivity for electrical current, the various substances are divided into conductors, non-conductors (insulators) and semiconductors. The three characteristic effects of current are

- generation of heat in conductors through which current passes
- the magnetic field associated with the current
- transport of substance by ion currents

The current intensity is determinded by the quantity of charge flowing through the conductor during a certain time. It results from the relation I = Q/t. The unit of current intensity is the ampere = A; the most frequently used sub-units are kA, mA and µA.

From the definition equation of the current intensity, the basic unit for the quantity of electricity is derived; it is the ampere-second (A.s) = coulomb (C). A frequently used sub-unit is the ampere-hour (A.h).

Questions and problems:

1. How many A are 27 mA; 5,1 kA; 80 µA; 1,000 mA; 6,500 µA; 0,04 kA

2. How many C are

0,5 A.h; 84 A.h; 0,000278 A.h?

3. A quantity of electricity of 108,000 C is flowing through a line within 5 hours. Find the current intensity.

4. An electric current having the intensity of 2 A flows through a line for a period of 2 hours. Calculate the transported quantity of electricity in the units C and A.h.