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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

8.2. The Rotating Field

The most important property of the three-phase current is discussed here. For this purpose, we again start from three coils displaced by 120° from each other which are connected to a three-phase current according to Fig. 8.3. (Fig. 8.4.).

Fig. 8.4. Three-phase winding of a motor

Fig. 8.5. Development of the rotating field

a) Three-phase line diagram with points of time plotted on the diagram

b) Resulting magnetic field for the points of time plotted on

In each of the three coils, an alternating field will be brough about in accordance with the alternating voltage applied. The total magnetic field resulting from the magnetic fields of the 3 coils is subject to a closer examination below. For this purpose, we have to give some explanations regarding the representations. When the positive half wave of the alternating voltage is applied to the coil, a magnetic north pole will be formed at the end of the coil which is inside the arrangement in accordance with the sense of winding of the coil. This pole is represented by cross hatching. The density of the lines of hatching corresponds to the amplitude of the voltage present at the instant of observing. When the negative half wave is applied, the south pole is formed which is represented by longitudinal hatching. For the points of time entered into the three-phase current line diagram in Fig. 8.5.a, the magnetic flux produced in the three coils at the points of time a to g is shown in Fig. 8.5.b. The position of the total magnetic field brought about by the three individual fields is represented by the position of a rod magnet whose north pole is marked black. (A representation of the coils as given in Fig. 8.4. is omitted for the sake of clearness.) The position of the total magnetic field changes with the interval of time under consideration of the three-phase current line diagram. It is evident that the total magnetic field has turned through half a revolution from point of time a to point of time g. When further partial pictures would be represented, then a full revolution of the total magnetic field would be performed during the duration of a cycle of the three-phase current. This shows that, in a three-phase winding connected to three-phase current, a rotating magnetic field is formed which is called rotating field. The majority of electric motors and their mode of operation are based on the presence of the rotating field which enables extremely simple and sturdy designs of electric motors. Within a full cycle of the three-phase current one revolution of the rotating field is performed in an arrangement according to Fig. 8.5. When two times three coils are arranged at the circumference, then the rotating field will perform only half a revolution within one cycle. Such an arrangement is termed as design with two pairs of poles. There are also arrangements with a higher number of pole pairs. For the calculation of the rotational speed of the rotating field we have

nD = f/p




rotational speed of the rotating field




number of pole pairs

Example 8.1.

A three-phase current winding (also known as polyphase winding) with three pairs of poles is connected to a three-phase current having a frequency of 50 Hz. Determine the rotational speed of the rotating field per minute!


f = 50 Hz
p =3

To be found:

nD in rpm


nD = f/p
nD = (50 1/s)/3

Since the speed per minute is required, the above calculation will, however, result in the revolutions per second, multiplying by 60 s/min is necessary.

nD = (50 1/s · 60 s/min)/3
nD = 1000 rpm

The rotating field has a speed of 1000 revolutions per minute.

When exchanging two phases shown in Fig. 8.5. in the manner represented in Fig. 8.6., the sense of rotation of the rotating field is inverted. This property of the three-phase current is also of advantage to the construction of electric motors.

Fig. 8.6. Three-phase winding with the phases exchanged as compared to Fig. 8.5.

Inside a polyphase winding connected to three-phase current a rotating field is formed (rotating magnetic field) whose sense of rotation can be inverted by exchanging two connections. The rotational speed of the rotating field is dependent on the frequency and the number of pole pairs. Simple designs of motors are possible due to the rotating field involved in three-phase current.

Questions and problems:

1. Under which conditions is a rotating field formed?

2. Demonstrate the reversal of the sense of rotation due to the exchange of two phases as shown in Fig. 8.6. with the help of a representation as given in Fig. 8.5.b!

3. What is the technical importance of the rotating field?

4. Calculate the possible rotational speeds of the rotating field for arrangements with 1 to 10 pairs of poles when the frequency is 50 Hz!