Electrical quantities underpin all modern technology and infrastructure, from powering county government offices to enabling ICT systems in universities and ensuring proper lighting in retail businesses. Understanding these quantities and their units is critical for professionals across sectors to design, maintain, and troubleshoot electrical systems safely and efficiently. This chapter introduces the fundamental SI units used in electrical engineering and explores the materials that conduct or resist electric current, providing a basis for practical electrical applications in diverse Kenyan workplaces.

1.1 Basic SI Units

In Kenya’s dynamic industries, precise measurement of electrical quantities ensures the reliability and safety of equipment used in hospitals, banks, farms, and hotels. The International System of Units (SI) provides standard units for quantifying electrical parameters such as current, voltage, resistance, and power, which are essential for interpreting and designing electrical circuits across sectors.

1.1.1 Current and Its Unit

Electric current represents the flow of electric charge through a conductor and is fundamental to powering devices in institutions such as SACCO offices or county referral hospitals. The SI unit of electric current is the ampere (A).

The current \(I\) is defined by the rate of flow of charge \(Q\) over time \(t\):

$$ I = \frac{Q}{t} $$

Worked Examples

Example 1: A clinic uses a device that allows \(30\) coulombs of charge to pass through its circuit in \(10\) seconds. Find the electric current.

Given: \(Q = 30\,C\), \(t = 10\,s\)

$$ I = \frac{Q}{t} $$

$$ I = \frac{30}{10} $$

$$ I = 3\,A $$

Answer: 3 amperes

Example 2: A banking system's UPS draws a current of \(5\,A\). How much charge passes through the system in \(2\) minutes?

Given: \(I = 5\,A\), \(t = 2\, \text{minutes} = 120\,s\)

$$ Q = I \times t $$

$$ Q = 5 \times 120 $$

$$ Q = 600\,C $$

Answer: 600 coulombs

Example 3: A solar-powered water pump on a farm operates with a current of \(2.5\,A\) for \(4\) hours. Calculate the total charge transferred.

Given: \(I = 2.5\,A\), \(t = 4\, \text{hours} = 4 \times 3600 = 14400\,s\)

$$ Q = I \times t $$

$$ Q = 2.5 \times 14400 $$

$$ Q = 36000\,C $$

Answer: 36,000 coulombs

1.1.2 Voltage and Its Unit

Voltage is the electric potential difference that causes current to flow in a circuit. It is the driving force behind electrical energy transfer in county government offices or university laboratories. The SI unit of voltage is the volt (V).

Voltage \(V\) is defined as the energy \(W\) per unit charge \(Q\):

$$ V = \frac{W}{Q} $$

Worked Examples

Example 1: A hospital battery supplies \(2400\,J\) of energy to \(120\,C\) of charge. Find the voltage.

Given: \(W = 2400\,J\), \(Q = 120\,C\)

$$ V = \frac{W}{Q} $$

$$ V = \frac{2400}{120} $$

$$ V = 20\,V $$

Answer: 20 volts

Example 2: An ICT center uses a power supply that provides \(12\,V\) across a device when \(144\,J\) of energy is transferred. Calculate the charge moved.

Given: \(V = 12\,V\), \(W = 144\,J\)

$$ Q = \frac{W}{V} $$

$$ Q = \frac{144}{12} $$

$$ Q = 12\,C $$

Answer: 12 coulombs

Example 3: A lighting system in a hotel converts \(3600\,J\) of energy to light using a voltage of \(240\,V\). Find the charge transferred.

Given: \(W = 3600\,J\), \(V = 240\,V\)

$$ Q = \frac{W}{V} $$

$$ Q = \frac{3600}{240} $$

$$ Q = 15\,C $$

Answer: 15 coulombs

1.1.3 Resistance and Its Unit

Resistance measures how much a material opposes the flow of electric current, crucial for protecting equipment in schools and retail businesses from overload. The SI unit of resistance is the ohm (Ω).

Resistance \(R\) is related to voltage \(V\) and current \(I\) by Ohm’s Law:

$$ R = \frac{V}{I} $$

Worked Examples

Example 1: A cooperative uses a device with a voltage of \(12\,V\) and current of \(3\,A\). Calculate the resistance.

Given: \(V = 12\,V\), \(I = 3\,A\)

$$ R = \frac{V}{I} $$

$$ R = \frac{12}{3} $$

$$ R = 4\,\Omega $$

Answer: 4 ohms

Example 2: A bank’s security system has a resistance of \(8\,\Omega\) and operates at \(24\,V\). Find the current flowing.

Given: \(R = 8\,\Omega\), \(V = 24\,V\)

$$ I = \frac{V}{R} $$

$$ I = \frac{24}{8} $$

$$ I = 3\,A $$

Answer: 3 amperes

Example 3: An agricultural irrigation pump has a resistance of \(15\,\Omega\) and draws a current of \(2\,A\). Find the voltage across it.

Given: \(R = 15\,\Omega\), \(I = 2\,A\)

$$ V = I \times R $$

$$ V = 2 \times 15 $$

$$ V = 30\,V $$

Answer: 30 volts

1.1.4 Power and Its Unit

Power quantifies the rate of energy transfer in electrical devices, important in managing consumption in county referral hospitals and hotel kitchens. The SI unit of power is the watt (W).

Power \(P\) is related to voltage \(V\) and current \(I\) by:

$$ P = V \times I $$

Worked Examples

Example 1: A TVET college computer uses \(240\,V\) and draws \(2\,A\). Calculate the power consumed.

Given: \(V = 240\,V\), \(I = 2\,A\)

$$ P = V \times I $$

$$ P = 240 \times 2 $$

$$ P = 480\,W $$

Answer: 480 watts

Example 2: A retail business has a device consuming \(600\,W\) at \(120\,V\). Find the current it draws.

Given: \(P = 600\,W\), \(V = 120\,V\)

$$ I = \frac{P}{V} $$

$$ I = \frac{600}{120} $$

$$ I = 5\,A $$

Answer: 5 amperes

Example 3: A farm’s water pump uses \(10\,A\) current at \(220\,V\). Calculate the power.

Given: \(I = 10\,A\), \(V = 220\,V\)

$$ P = V \times I $$

$$ P = 220 \times 10 $$

$$ P = 2200\,W $$

Answer: 2200 watts

Chapter Summary

This chapter introduced the fundamental SI units essential for understanding electrical quantities, including power measured in watts, current in amperes, resistance in ohms, and voltage in volts. It explored the distinction between conductors and insulators by examining the properties of metals and non-metals and their roles in electrical circuits. The chapter then defined key electrical quantities such as charge, force, work, and power, and demonstrated calculations involving these concepts. Ohm's Law was presented as a critical principle linking voltage, current, and resistance, with practical calculation examples to reinforce comprehension. Measurement techniques were covered, focusing on the use of multimeters, oscilloscopes, and ammeters to obtain accurate electrical readings. Finally, the importance of proper measurement calibration was emphasized to ensure precision and reliability in electrical and electronic testing. Through these topics, the chapter provided a comprehensive foundation for applying basic electrical concepts in practical settings.