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Chapter 1
Electrical fundamentals
Chapter summary
This chapter has been designed to provide you with the background knowledge required to help you understand the concepts introduced in the later chapters. If you have studied electrical science, electrical principles or electronics beyond school level then you will already be familiar with many of these concepts. If, on the other hand, you are returning to study or are a newcomer to electronics or electrical technology this chapter will help you get up to speed.
Fundamental units
You will already know that the units that we now use to describe such things as length, mass and time are standardized within the International System of Units. This SI system is based upon the seven fundamental units (see Table 1.1).
Derived units
All other units are derived from these seven fundamental units. These derived units generally have their own names and those commonly encountered in electrical circuits are summarized in Table 1.2 together with the corresponding physical quantities.
If you find the exponent notation shown in Table 1.2 a little confusing, just remember that V−1 is simply 1/V, s−1 is 1/s, m−2 is 1/m−2, and so on.
Example 1.1
The unit of flux density (the Tesla) is defined as the magnetic flux per unit area. Express this in terms of the fundamental units.
Solution
The SI unit of flux is the Weber (Wb). Area is directly proportional to length squared and, expressed in terms of the fundamental SI units, this is square metres (m2). Dividing the flux (Wb) by the area (m2) gives Wb/m2 or Wb m−2. Hence, in terms of the fundamental SI units, the Tesla is expressed in Wb m−2.
Table 1.1 SI units
| Quantity | Unit | Abbreviation |
| Current | ampere | A |
| Length | metre | m |
| Luminous intensity | candela | cd |
| Mass | kilogram | kg |
| Temperature | Kelvin | K |
| Time | second | s |
| Matter | mol | mol |
Table 1.2 Electrical quantities
| Quantity | Derived unit | Abbreviation | Equivalent (in terms of fundamental units) |
| Capacitance | Farad | F | A s V-1 |
| Charge | Coulomb | C | A s |
| Energy | Joule | J | N m |
| Force | Newton | N | kg m s-1 |
| Frequency | Hertz | Hz | s-1 |
| Illuminance | Lux | lx | lm m-2 |
| Inductance | Henry | H | V s A-1 |
| Luminous flux | Lumen | lm | cd sr |
| Magnetic flux | Weber | Wb | V s |
| Potential | Volt | V | W A-1 |
| Power | Watt | W | J s-1 |
| Resistance | Ohm | Ω | V A-1 |
Example 1.2
The unit of electrical potential, the volt (V), is defined as the difference in potential between two points in a conductor which, when carrying a current of one amp (A), dissipates a power of one watt (W). Express the volt (V) in terms of joules (J) and coulombs (C).
Solution
In terms of the derived units:
Note that: watts = joules/seconds and also that amperes × seconds = coulombs
Alternatively, in terms of the symbols used to denote the units:
Hence, one volt is equivalent to one joule per coulomb.
Measuring angles
You might think it strange to be concerned with angles in electrical circuits. The reason is simply that, in analogue and a.c. circuits, signals are based on repetitive waves (often sinusoidal in shape). We can refer to a point on such a wave in one of two basic ways, either in terms of the time from the start of the cycle or in terms of the angle (a cycle starts at 0° and finishes as 360° (see Fig. 1.1)). In practice, it is often more convenient to use angles rather than time; however, the two methods of measurement are interchangeable and it’s important to be able to work in either of these units.
In electrical circuits, angles are measured in either degrees or radians (both of which are strictly dimensionless units). You will doubtless already be familiar with angular measure in degrees where one complete circular revolution is equivalent to an angular change of 360°. The alternative method of measuring angles, the radian, is defined somewhat differently. It is the angle subtended at the centre of a circle by an arc having length which is equal to the radius of the circle (see Fig. 1.2).
You may sometimes find that you need to convert from radians to degrees, and vice versa. A complete circular revolution is equivalent to a rotation of 360° or 2π radians (note that π is approximately equal to 3.142). Thus one radian is equivalent to 360/2π degrees (or approximately 57....
