Motivation

Electrical engineering permeates virtually every aspect of modern life. Its scope ranges from energy supply and control engineering to information technology. Whether smartphones, cars, or modern household appliances—every day we rely on countless devices that would be inconceivable without this discipline. Over the past decades, electrical engineering has enabled groundbreaking innovations and remains the driving force behind numerous technological developments. In the field of renewable energy, photovoltaic systems, wind turbines, and smart grids are based on advanced electrical engineering principles. Within the Internet of Things (IoT), the networking of everyday objects relies on miniaturised sensors, microcontrollers, and communication modules. Likewise, the development of powerful AI systems would not be possible without specialised hardware components such as GPUs and CPUs. Expertise in this field is not only essential for electrical engineering students. The relevance of its fundamental concepts is steadily increasing for students across all engineering and related disciplines. Modern product development is driven by interdisciplinary project teams.

• Mechanical engineering: Even if mechanical engineers are not directly involved in the development of electrical/electronic components, they need a basic understanding of the colleagues involved in the development project. For example, in the development of robot systems or automated production facilities, close cooperation between mechanical engineering and electrical engineering is essential.
• Computer science: The interface between hardware and software is becoming increasingly important. Computer scientists must understand how their programmes interact with the underlying electronics.
• Medical technology: Modern medical devices such as MRI scanners and pacemakers would be inconceivable without in-depth electrical engineering knowledge.

This script supports students in learning the necessary fundamentals. It not only imparts theoretical knowledge, but also demonstrates practical applications and interdisciplinary connections. The aim is to create a solid foundation on which students from various engineering disciplines can build. The concepts learned here form the basis for understanding more complex systems and prepare students for the challenges of an increasingly digitalised and networked world. From the basics of electricity to advanced topics such as signal processing and control engineering, this script lays the foundation for a successful career in a world that is significantly shaped by electrical engineering.

Physical quantities - definitions and units of measurement

1 The SI system of units

Every physical quantity is always described as a combination of a numerical value (measurement) and its unit of measurement (also called dimension). A few unitless quantities are an exception here; the unit of measurement for these is ‘1’. If necessary, the unit can be preceded by the abbreviation of a power of ten, which scales the numerical value (see section Zehnerpotenzen). The numerical value and the unit are separated by a space. Example: \(1000\,\mathrm {m} = 1\,\mathrm {km}\).

These units are defined in the international system of units, the SI system (Système International), and form the basis of all physical quantities. There are seven SI base quantities, which can be defined with the aid of fundamental physical constants. These constants can be determined experimentally with sufficient accuracy to form a reliable basis for our entire system of units. In addition to the base units defined in this way, there are other, so-called derived units, which can be traced back to the base units.

Apart from the SI system and its derived units, there are a number of other units, such as the Anglo-Saxon units pound, inch or mile, which are not used here.

The currently valid definitions of the units listed in the table above are:

• A second is 9,192,631,770 times the period duration of the hyperfine transition \(\Delta \nu \) in the caesium atom. \( ^{133}Cs.\)
• One metre is the length of the distance travelled by light in a vacuum during the time \(t = \frac {1}{299,792,458}\) s.
• Since May 2019, the kilogram has been dependent on the precisely defined Planck constant: \(1 \mathrm {kg} = \frac {h}{6.626 070 15\cdot 10^-{34}} \frac {\mathrm {s}}{\mathrm {m}^2}\)
• Since 2019, the ampere has been defined by the elementary charge. One ampere is the current flow of \(\frac {e}{1.602176634} \cdot 10^{-19} \frac {1}{\mathrm {s}}\) elementary charges per second.
• One Kelvin corresponds to a change in thermodynamic temperature that is accompanied by a change in thermal energy (\(kT\)) of \(1.380649 \cdot 10^{-23} \, \mathrm {J}\).
• A mole is the amount of substance in a system that contains \(6.022 140 76 \cdot 10^{23}\) of a specific individual particle.
• A candela is the luminous intensity of a radiation source that emits at a frequency of 540 THz and has a radiation intensity in this direction of \(\frac {1}{683} \frac {\mathrm {W}}{\mathrm {sr}}\).

The natural constants used to define the SI system are:

• Hyperfine transition: \( ^{133} Cs \Delta v = 9.192.631.770\,\mathrm {Hz}\)
• Speed of light: \(c = 299.792.458\,\frac {\mathrm {m}}{\mathrm {s}}\)
• Planck’s constant: \(h = 6,626 070 15 \cdot 10^{-34}\,\mathrm {Js}\)
• Elementary charge: \(e = 1,602 176 634 \cdot 10^{-19}\,\mathrm {As}\)
• Boltzmann constant: \(k_\mathrm {B} = 1,380 649 · 10^{-23} \, \frac {\mathrm {kg \cdot m^2}}{\mathrm {s^2 \cdot K}} \)
• Avogadro’s number: \(N_\mathrm {A} = 6,022 140 76 \cdot 10^{23}\,\frac {1}{\mathrm {mol}}\)
• Photometric radiation equivalent of monochromatic radiation of frequency \(540\,\mathrm {THz}\): \(K_\mathrm {cd}(540\,\mathrm {THz}) = 683 \, \frac {\mathrm {lm}}{\mathrm {W}}\)

Derived SI units  

From these seven basic units, a further 22 units with their own designations are derived. Some examples that are important for electrical engineering are listed below.:

Important: In equations involving physical quantities, both numerical values and units of measurement appear on both sides of the equal sign. Checking that the units are equal (if in doubt, broken down to the SI base units) is often a good way of checking the plausibility of the calculation.

2 Powers of ten

For better readability of very small or large numerical values, units can be scaled by powers of ten. To do this, the name of the power of ten is written directly in front of the unit without spaces. Often, the power of ten is chosen so that the number before the decimal point has as few digits as possible.

Another way to improve readability is to use exponential notation. This involves multiplying the measured value directly by the corresponding power of ten. The number of decimal places used must make physical sense. If nothing else is known, two decimal places are usually used.

Please note: When specifying weights, prefixes are not applied to the SI base unit kilogram (kg), but to the unit gram (g).

For units with exponents, such as area or volume units, the scaling prefix always refers to the base unit, so it must also be raised to the power.

\begin {align*} 1 \, \mathrm {m^1} &= 100^1 \cdot 10^{-2} \, \mathrm {m} = 100 \, \mathrm {cm} \\ 1 \, \mathrm {m^2} &= 100^2 \cdot (10^{-2} \, \mathrm {m})^2 = 10.000 \, \mathrm {cm^2} \\ 1 \, \mathrm {m^3} &= 100^3 \cdot (10^{-2} \, \mathrm {m})^3 = 1.000.000 \, \mathrm {cm^3} \end {align*}