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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

4.2. Efficiency

A conversion of energy without loss is not possible. For example, the electrical energy fed to a motor is converted not only into mechanical energy but also in heat due to the rise in temperature of the motor. Since this heating is not desired, this portion of the fed electrical energy which is converted into heat energy is called energy loss or lost energy. The efficienca is defined as the ratio of the energy delivered by the device to the energy supplied to it.

h = We/Wi = (Pe · t)/(Pi · t) = Pe/Pi

(4.4.)

where:

h 1)

efficiency

We

effective energy (energy delivered)

W1

indicated energy (energy supplied)

Pe

effective power

Pi

indicated power

Since the delivered energy is always smaller by the lost energy than the supplied energy, the efficiency is always smaller than 1. According to equation (4.4,), the same statement applies to power. When the losses are small, the efficiency will have a high value. The developmental level of a device is substantially determined by the magnit de of the efficiency. Great efforts are made to further improve the efficiency in order to convert the supplied energy into the desired energy with losses a small as possible.

Table 4.2. shows a few typical examples of the values involved.

Table 4.2. Efficiency of Selected Technical Equipment

Equipment

mean efficiency

incandescent lamp

0.05

steam locomotive

0.2

small electric motor

0.5

large electric motor

0.85

transformer

0.95

power station generator

0.98

1) h Greek letter eta

In many cases, several devices having a certain efficiency each are connected together and then the total efficiency of the arrangement is of interest. Fig. 4.1. shows an example. The arrangement shown may be, for example, a motor generator where device A is the electric motor, which takes up Psupplied 1 as electrical power and delivers Pdelivered 1 as mechanical power. At the same time Pdelivered 1 is the drive power supplied to the generator (device B) designated as Psupplied 2. The power delivered by the generator is designated as Pdelivered 2. The motor has the efficiency h1 and the generator the efficiency h2. The total efficiency is expressed as

h = Pdel2/Psupp1


Fig. 4.1. Interaction of two technical devices

P = Pzu; P = Pab

When inverting the relation

h2 = Pdel2/Psupp2 for Psupp2 and h1 = Pdel1/Psupp1 for Psupp1, we obtain

Pdel2 = h2 · Psupp2 and

Psupp1 = Pdel1/h1

Substituted into the initial equation we obtain

h = (h2 · Psupp2 · h1)/Pdel1

Since, however, Pdel1 = Psupp2, it follows that

h = h1 · h2

(4.5)

This shows that the total efficiency is equal to the product of the individual efficiencies and, thus, always smaller than the smallest individual efficiency.

Example 4.4.

The motor of a motor generator has an efficiency of 0.8 and the generator an efficiency of 0.75. What is the total efficiency?

Given:

h1 = 0.8
h2 = 0.75

To be found:

h

Solution:

h = h1 · h2
h = 0.8 · 0.75
h = 0.6

The total efficiency is 0.6.

In any energy conversion process, losses occur. This fact is described, by the efficiency. The conversion losses should be as small as possible; this is expressed by a value of the efficiency near 1. The efficienca is always smaller than 1. The total efficiency is the product of the individual efficiencies.

Questions and problems:

1. Why calls technical progress for an increase in the efficiency?

2. Give proof of the fact that for three devices connected together the total efficiency is: = h1 · h2 · h3.

3. A motor delivers a mechanical power of 650 W. What is its efficiency when the current input is 3.5 A at a voltage of 220 V?

4. A motor generator has an input of 3 A while connected to a voltage of 220 V and delivers a voltage of 48 V to the generator. The motor has an efficiency of 0.8 and the generator of 0.78. What is the current drawn from the generator?