This chapter introduces the fundamental electrical quantities essential for understanding and applying electrical principles across various professional fields in Kenya. Mastery of these quantities enables technicians, administrators, and professionals in healthcare, education, business, agriculture, and environmental management to interpret electrical data correctly and perform related calculations confidently. Accurate application of these concepts supports efficient energy use, safety, and maintenance of electrical systems widely used in hospitals, banks, universities, farms, and government offices.

1.1 Basic SI Units

Basic electrical quantities are measured using the International System of Units (SI). These units provide a standardized way to express electrical parameters such as voltage, current, resistance, power, and energy. Understanding these units and their relationships is crucial for professionals working with electrical devices, ensuring consistency and accuracy in measurements and calculations.

1.1.1 Overview of SI Units

Electrical quantities have standard SI units and symbols that allow for clear communication and calculation. A welder in one county and an engineer in another who both read "230 V" or "5 A" understand exactly the same thing, because the unit and its symbol are fixed internationally. Each unit is named after a scientist, so its symbol is written with a capital letter (V, A, W, Ω), while the quantity symbol is usually in italics or a different letter (V, I, P, R).

The main electrical quantities include:

• Voltage (V): Measures electrical potential difference in volts (V). It represents the energy per unit charge.
• Current (I): Measures electrical flow in amperes (A). It indicates the rate of charge flow.
• Resistance (R): Measures opposition to current flow in ohms (Ω).
• Power (P): Measures the rate of energy transfer in watts (W).
• Energy (E): Measures electrical work done or energy consumed in joules (J) or kilowatt-hours (kWh).

The sections below treat each quantity in turn, with its definition, formulas and worked examples.

1.1.1.1 Power (Watts, W)

Power is the rate at which electrical energy is converted into another form, such as heat, light or motion. Its SI unit is the watt (W), defined as one joule of energy transferred every second (1 W = 1 J/s). Power tells you how hard a device is working: a 60 W lamp converts energy twice as fast as a 30 W lamp.

Power can be calculated from any two of voltage, current and resistance:

• P = V × I (when voltage and current are known)
• P = I² × R (when current and resistance are known)
• P = V² ÷ R (when voltage and resistance are known)

Large and small powers are written with prefixes: 1 kW = 1000 W, 1 MW = 1 000 000 W and 1 mW = 0.001 W.

Example: A bench grinder in a welding workshop operates at 230 V with a current of 5 A. What is the power consumption?

Given: V = 230 V, I = 5 A

Formula: P = V × I

Substitution: P = 230 × 5

Calculation: P = 1150 W

Answer: 1150 W

Example: A 100 Ω heating element in an electrode drying oven is connected to 230 V. Calculate the power dissipated.

Given: R = 100 Ω, V = 230 V

Formula: P = V² ÷ R

Substitution: P = 230² ÷ 100

Calculation: P = 52 900 ÷ 100 = 529 W

Answer: 529 W

Example: A workshop extension cable feeding a welding machine has a resistance of 0.5 Ω and carries 20 A. Calculate the power lost as heat in the cable.

Given: R = 0.5 Ω, I = 20 A

Formula: P = I² × R

Substitution: P = 20² × 0.5

Calculation: P = 400 × 0.5 = 200 W

Answer: 200 W

1.1.1.2 Current (Amperes, A)

Electric current is the rate at which electric charge flows past a point in a circuit. Its SI unit is the ampere (A), defined as a flow of one coulomb of charge per second (1 A = 1 C/s). The relationship is I = Q ÷ t, where Q is charge in coulombs (C) and t is time in seconds (s). By convention, current is drawn flowing from the positive terminal of a source to the negative terminal, even though electrons actually move the opposite way.

Small currents are expressed in milliamperes (1 mA = 0.001 A) and microamperes (1 µA = 0.000001 A), which is common in electronic circuits. Current is measured with an ammeter connected in series with the load, so that the same current passes through the meter and the load.

Example: A 50 Ω heater element in a welding workshop is connected to a 240 V supply. Calculate the current flowing.

Given: R = 50 Ω, V = 240 V

Formula: I = V ÷ R

Substitution: I = 240 ÷ 50

Calculation: I = 4.8 A

Answer: 4.8 A

Example: A workshop's backup battery supplies a steady 3 A to emergency lighting for 2 hours. Calculate the charge delivered.

Given: I = 3 A, t = 2 h = 2 × 3600 = 7200 s

Formula: Q = I × t

Substitution: Q = 3 × 7200

Calculation: Q = 21 600 C

Answer: 21 600 C

1.1.1.3 Resistance (Ohms, Ω)

Resistance is the opposition a material or component offers to the flow of electric current. Its SI unit is the ohm (Ω), defined as the resistance that allows one ampere to flow when one volt is applied across it (1 Ω = 1 V/A). Resistance is calculated as R = V ÷ I. Resistance converts electrical energy into heat, which is useful in a heater element and wasteful in a long, thin cable.

The resistance of a conductor depends on its material, its length, its cross-sectional area and its temperature. A longer or thinner conductor has more resistance than a shorter or thicker one of the same material. Values are written with prefixes such as the kilohm (1 kΩ = 1000 Ω) and the megohm (1 MΩ = 1 000 000 Ω).

Example: The heating element of a flux-drying cabinet in a welding workshop draws 10 A when connected to a 230 V supply. Calculate its resistance.

Given: V = 230 V, I = 10 A

Formula: R = V ÷ I

Substitution: R = 230 ÷ 10

Calculation: R = 23 Ω

Answer: 23 Ω

1.1.1.4 Voltage (Volts, V)

Voltage, or potential difference, is the energy given to each unit of charge as it moves between two points in a circuit. Its SI unit is the volt (V), defined as one joule of energy per coulomb of charge (1 V = 1 J/C). The relationship is V = W ÷ Q, where W is energy in joules and Q is charge in coulombs. Voltage is the "push" that drives current through a circuit: without a potential difference, no current flows.

Voltage is produced by sources such as cells, batteries, solar panels and generators. It is measured with a voltmeter connected in parallel across the component being tested. Prefixes include the millivolt (1 mV = 0.001 V) and the kilovolt (1 kV = 1000 V).

Example: In a welding workshop, an extraction fan motor circuit transfers 460 J of energy to 2 C of charge. Calculate the voltage.

Given: W = 460 J, Q = 2 C

Formula: V = W ÷ Q

Substitution: V = 460 ÷ 2

Calculation: V = 230 V

Answer: 230 V

Example: The indicator circuit of a welding machine has a 6 Ω resistor carrying a current of 2 A. Calculate the voltage across the resistor.

Given: R = 6 Ω, I = 2 A

Formula: V = I × R

Substitution: V = 2 × 6

Calculation: V = 12 V

Answer: 12 V

Energy (joules and kilowatt-hours)

Energy is the total electrical work done or consumed over a period of time. Its SI unit is the joule (J), where one joule is the energy used by a 1 W device in 1 second. Because the joule is very small for everyday use, electricity supply is billed in kilowatt-hours (kWh), the energy used by a 1 kW load running for one hour. The relationship is E = P × t, and 1 kWh = 1000 W × 3600 s = 3 600 000 J.

Example: A welding workshop uses a 500 W electrode drying heater for 3 hours. Calculate the energy consumed in kilowatt-hours (kWh), and the cost at an assumed rate of Ksh 25 per kWh.

Given: P = 500 W = 0.5 kW, t = 3 h

Formula: E = P × t

Substitution: E = 0.5 × 3

Calculation: E = 1.5 kWh

Cost: 1.5 × 25 = Ksh 37.50

Answer: 1.5 kWh, costing Ksh 37.50

Example: An angle grinder in a welding workshop draws 3 A at 240 V. Calculate the power and the energy consumed in 5 hours.

Given: I = 3 A, V = 240 V, t = 5 h

Power formula: P = V × I

Substitution: P = 240 × 3

Calculation: P = 720 W = 0.72 kW

Energy formula: E = P × t

Substitution: E = 0.72 × 5

Calculation: E = 3.6 kWh

Answer: Power = 720 W, Energy = 3.6 kWh

SI prefixes and unit conversion

Electrical values range from tiny sensor currents to very large generator outputs, so SI prefixes are used to avoid writing long strings of zeros. Before substituting into a formula, convert every value to the base unit (volts, amperes, ohms, watts, seconds), otherwise the answer will be wrong by a factor of 1000 or more.

Example: A 4.7 kΩ resistor on the electronic control board of a welding machine is connected across a 9 V battery during testing. Calculate the current in milliamperes.

Given: R = 4.7 kΩ = 4700 Ω, V = 9 V

Formula: I = V ÷ R

Substitution: I = 9 ÷ 4700

Calculation: I = 0.001 915 A = 1.9 mA (to 2 significant figures)

Answer: 1.9 mA

Chapter Summary

This chapter introduced the fundamental SI units used in electrical measurements, focusing on power measured in watts, current in amperes, resistance in ohms, and voltage in volts. It explained the distinction between conductors and insulators by examining their characteristics, highlighting the difference between metals and non-metals and their roles in electrical circuits. Key electrical quantities such as charge, force, work, and power were defined along with their units, and calculations involving these quantities were demonstrated. Ohm's Law was presented as a core principle relating voltage, current, and resistance, with practical applications and calculation examples. The chapter also covered essential measurement techniques in electrical and electronic contexts, emphasizing the correct use of multimeters and ammeters. Finally, the importance of calibration in ensuring accurate electrical measurements was discussed to maintain reliability and precision in practical work.