Electrical principles underpin all electronics engineering disciplines in Kenya, where precise measurement and application of electrical quantities are essential for designing, testing, and maintaining electronic systems. This chapter focuses on applying electrical quantities using the International System of Units (SI), the global standard for measurement that ensures consistency and accuracy in engineering calculations. Mastery of SI units is critical for professionals working in electronics industries such as telecommunications, manufacturing, and renewable energy systems in Kenya, where adherence to international standards is mandatory for quality and safety. Understanding these units enables engineers to communicate effectively, analyze circuits, and develop reliable electronic devices.

1.1 The Meaning of SI Unit

The International System of Units (SI) is the internationally accepted system for measuring physical quantities, including those used in electronics engineering. Kenya’s electronics engineers rely on SI units to quantify voltage, current, resistance, capacitance, and other electrical parameters with precision and uniformity. This system simplifies collaboration, documentation, and compliance with regulatory standards in the electronics sector. The following subtopics explain SI units’ foundations, base units, derived units, and prefixes relevant to electronics engineering.

1.1.1 Concept and Definition of SI Units

SI units represent a coherent system of measurement used worldwide to standardize quantities in science and engineering. The system is built on seven base units from which all other units are derived, enabling unambiguous expression of physical quantities.

$$ \text{SI Unit} = \text{Standardized measure of a physical quantity based on agreed definitions} $$

Worked Examples

Example 1: Calculate the value of current if 5 coulombs of charge pass through a conductor in 2 seconds.
Given: Charge \(Q = 5\,C\), Time \(t = 2\,s\)$$ I = \frac{Q}{t} $$$$ I = \frac{5}{2} $$$$ I = 2.5\,A $$ Answer: 2.5 amperes (A)

Example 2: Find the voltage across a resistor when a current of 3 A flows through a resistance of 4 Ω.
Given: Current \(I = 3\,A\), Resistance \(R = 4\,\Omega\)$$ V = I \times R $$$$ V = 3 \times 4 $$$$ V = 12\,V $$ Answer: 12 volts (V)

Example 3: Determine the resistance of a conductor if a voltage of 24 V causes a current of 6 A to flow.
Given: Voltage \(V = 24\,V\), Current \(I = 6\,A\)$$ R = \frac{V}{I} $$$$ R = \frac{24}{6} $$$$ R = 4\,\Omega $$ Answer: 4 ohms (Ω)

1.1.2 Base SI Units Relevant to Electronics Engineering

The SI system defines seven base units; in electronics, four are most commonly used: ampere (A), volt (V), ohm (Ω), and second (s). These units form the foundation for describing electrical phenomena.

$$ \text{Base SI Units in Electronics:} \quad \text{Ampere (A), Second (s), Meter (m), Kilogram (kg)} $$

Worked Examples

Example 1: Calculate the charge in coulombs if a current of 2 A flows for 10 seconds.
Given: \(I = 2\,A\), \(t = 10\,s\)$$ Q = I \times t $$$$ Q = 2 \times 10 $$$$ Q = 20\,C $$ Answer: 20 coulombs (C)

Example 2: A wire of length 3 m carries a current of 5 A. Calculate the total charge passing through a cross-section in 4 seconds.
Given: \(I = 5\,A\), \(t = 4\,s\)$$ Q = I \times t $$$$ Q = 5 \times 4 $$$$ Q = 20\,C $$ Answer: 20 coulombs (C)

Example 3: Find the time taken for a charge of 15 C to pass through a conductor carrying 3 A current.
Given: \(Q = 15\,C\), \(I = 3\,A\)$$ t = \frac{Q}{I} $$$$ t = \frac{15}{3} $$$$ t = 5\,s $$ Answer: 5 seconds (s)

1.1.3 Derived SI Units Used in Electronics

Derived units are combinations of base units that describe complex electrical quantities such as voltage, resistance, capacitance, and inductance. These units are essential for characterizing electronic components and circuits.

$$ \text{Example:} \quad \text{Volt (V)} = \frac{\text{kg} \times \text{m}^2}{\text{s}^3 \times \text{A}} $$

Worked Examples

Example 1: Calculate the power dissipated in a resistor of 8 Ω when a current of 2 A flows through it.
Given: \(R = 8\,\Omega\), \(I = 2\,A\)$$ P = I^2 \times R $$$$ P = 2^2 \times 8 $$$$ P = 4 \times 8 $$$$ P = 32\,W $$ Answer: 32 watts (W)

Example 2: Find the capacitance of a capacitor if it stores 0.002 coulombs of charge when 5 volts are applied.
Given: \(Q = 0.002\,C\), \(V = 5\,V\)$$ C = \frac{Q}{V} $$$$ C = \frac{0.002}{5} $$$$ C = 0.0004\,F $$ Answer: 0.0004 farads (F)

Example 3: Calculate the inductance of a coil if the induced voltage is 0.03 V when the current changes at a rate of 0.005 A/s.
Given: \(V = 0.03\,V\), \(\frac{dI}{dt} = 0.005\,A/s\)$$ L = \frac{V}{\frac{dI}{dt}} $$$$ L = \frac{0.03}{0.005} $$$$ L = 6\,H $$ Answer: 6 henrys (H)

1.1.4 SI Unit Prefixes and Their Application in Electronics

SI prefixes denote multiples or fractions of base units to express very large or very small quantities conveniently. Electronics engineers in Kenya frequently use prefixes such as milli, micro, kilo, and mega for components like resistors, capacitors, and inductors.

$$ \text{Unit with prefix} = \text{Prefix factor} \times \text{Base unit} $$

Worked Examples

Example 1: Convert 4700 milliohms to ohms.
Given: \(4700\,m\Omega\)$$ 1\,m\Omega = 10^{-3}\,\Omega $$$$ 4700\,m\Omega = 4700 \times 10^{-3}\,\Omega $$$$ 4700\,m\Omega = 4.7\,\Omega $$ Answer: 4.7 ohms (Ω)

Example 2: Express 0.000002 farads in microfarads.
Given: \(0.000002\,F\)$$ 1\,\mu F = 10^{-6}\,F $$$$ 0.000002\,F = \frac{0.000002}{10^{-6}}\,\mu F $$$$ 0.000002\,F = 2\,\mu F $$ Answer: 2 microfarads (μF)

Example 3: Convert 3.3 kiloamperes to amperes.
Given: \(3.3\,kA\)$$ 1\,kA = 10^{3}\,A $$$$ 3.3\,kA = 3.3 \times 10^{3}\,A $$$$ 3.3\,kA = 3300\,A $$ Answer: 3300 amperes (A)

Chapter Summary

This chapter began by explaining the meaning of the International System of Units (SI units), highlighting their universal role in standardizing measurements. It then detailed the SI units associated with various electrical parameters such as voltage, current, resistance, and power. Ohm’s Law was introduced as a fundamental principle that relates voltage, current, and resistance in an electrical circuit. The chapter provided methods for performing calculations involving these electrical parameters, emphasizing practical problem-solving techniques. Additionally, it covered the different instruments used to measure electrical quantities, including voltmeters, ammeters, and ohmmeters, describing their functions and applications. Overall, the chapter established a solid foundation for understanding and working with electrical measurements in practical contexts.