Electrical Engineering Fundamentals

1. Scope, audience and safety boundary

Purpose and limits

This article explains introductory electrical relationships, common equipment functions and the evidence chain used to review installation, test and handover readiness. It does not replace electrical design, protection or fault studies, cable calculations, approved drawings, legislation, project specifications, manufacturer instructions, authorised switching procedures, jurisdiction-specific certification or competent-person review.

This is not an operational switching or energisation procedure. The approved project safety rules, risk assessment, permits, isolations, method, OEM requirements and authorised switching programme govern the activity.

2. Electrical quantities, symbols and SI units

A quantity describes what is measured, a symbol identifies it in an equation, and a unit provides the scale. Symbols can vary by context, so each calculation should define them.

Distinctions that matter

kW and kWh

Kilowatts express power at an instant; kilowatt-hours express accumulated energy.

Current and charge

Current is the rate of charge flow; charge is the electrical quantity transferred or stored.

Resistance and impedance

Resistance opposes current without representing phase behaviour; impedance is the complex AC relationship combining resistance and reactance.

Real, reactive and apparent power

Real power transfers net energy, reactive power represents alternating energy exchange, and apparent power combines both for equipment loading.

3. Voltage, current, resistance and Ohm’s law

Voltage is electric potential difference. Current is the rate of charge flow. Resistance describes opposition to current in the selected model.

V = IR   ·   I = V / R   ·   R = V / IVoltage equals current multiplied by resistance. Current equals voltage divided by resistance. Resistance equals voltage divided by current.

These forms apply where the element can be represented by a constant resistance under the stated operating conditions. Temperature, material behaviour, AC reactance, transient effects and non-linear loads can make the simple model unsuitable.

Worked example: With 24 V across 12 Ω, current is 24 ÷ 12 = 2 A. Power is 24 × 2 = 48 W.

4. Series and parallel circuits

Series paths

Current is common through ideal series elements. Source voltage equals the sum of voltage drops, and equivalent resistance is the sum of the individual resistances.

R_series = R₁ + R₂ + …   ·   V = V₁ + V₂ + …Equivalent series resistance equals the sum of the resistances. Total voltage equals the sum of the voltage drops.

Parallel branches

Voltage is common across ideal parallel branches. Total current is the sum of branch currents, and reciprocal conductances add.

I = I₁ + I₂ + …   ·   1 / R_parallel = 1 / R₁ + 1 / R₂ + …Total current equals the sum of branch currents. The reciprocal of equivalent parallel resistance equals the sum of reciprocal branch resistances.

Worked example: A 12 V source with 2 Ω and 4 Ω in series gives 6 Ω and 2 A; the drops are 4 V and 8 V. A separate 12 V circuit with 12 Ω and 6 Ω branches gives 4 Ω equivalent resistance and 3 A total current, split 1 A and 2 A.

These idealised relationships do not replace cable, voltage-drop, protection or fault studies for an actual installation.

5. DC power and electrical energy

P = VI   ·   P = I²R   ·   P = V² / R   ·   E = PtPower equals voltage multiplied by current. For a resistor, power equals current squared multiplied by resistance, or voltage squared divided by resistance. Energy equals power multiplied by time.

A watt is one joule per second. A kilowatt is 1,000 W. Watt-hours and kilowatt-hours express energy accumulated over time; the SI coherent energy unit is the joule.

Worked example: A constant 500 W load operating for 3 h uses 1,500 Wh, or 1.5 kWh. That energy value is not the instantaneous demand, which remains 500 W.

6. AC fundamentals

An alternating quantity changes magnitude and direction with time. One repeating pattern is a cycle; frequency is cycles per second and period is the time per cycle. Amplitude describes magnitude relative to a reference. Phase difference describes the angular displacement between waveforms.

For a sinusoidal waveform, the RMS value is the DC-equivalent value for the same heating effect in a resistor. RMS is not simply the arithmetic average of the alternating waveform. Fifty hertz and 60 Hz are common system frequencies, but neither is universal; the actual system rating controls.

T = 1 / fPeriod equals one divided by frequency.

7. Single-phase and three-phase power

Line quantities are measured between or in supply conductors; phase quantities relate to one winding or branch. Star and delta connections change the line-to-phase relationships. Actual design calculations require the applicable arrangement, waveform, load balance and governing standard.

Worked example: For 400 V line voltage, 32 A line current and power factor 0.85, balanced three-phase real power is √3 × 400 × 32 × 0.85 = 18,844.7 W, approximately 18.84 kW.

8. Real, reactive and apparent power

Real power P, measured in watts, represents net energy transfer. Reactive power Q, measured in vars, represents alternating energy exchange associated with reactive elements. Apparent power S, measured in volt-amperes, relates RMS voltage and current to equipment loading.

PF = P / S   ·   S² = P² + Q²Power factor equals real power divided by apparent power. For the power triangle, apparent power squared equals real power squared plus reactive power squared.

The right-angled power-triangle relationship describes sinusoidal steady-state conditions using compatible signs and magnitudes. Poor power factor can increase current for a given useful real power; tariff, correction and compliance consequences remain installation-specific.

9. Resistance, reactance and impedance

Inductance opposes changes in current and produces inductive reactance that rises with frequency. Capacitance stores electric-field energy and produces capacitive reactance whose magnitude falls with frequency.

X_L = 2πfL   ·   X_C = 1 / (2πfC)Inductive reactance equals two pi multiplied by frequency and inductance. Capacitive reactance magnitude equals one divided by two pi multiplied by frequency and capacitance.

Z = R + jX   ·   |Z| = √(R² + X²)Complex impedance equals resistance plus the imaginary unit multiplied by net reactance. Impedance magnitude equals the square root of resistance squared plus reactance squared.

Z is the complex quantity; |Z|the magnitude of impedance is its magnitude. Sign conventions for inductive and capacitive reactance must be stated, and harmonic or transient behaviour may require a more detailed model.

10. Transformers

A transformer transfers AC energy electromagnetically between primary and secondary windings. The turns ratio establishes the ideal voltage ratio and inverse current ratio, enabling step-up, step-down and isolation functions.

V_p / V_s = N_p / N_s   ·   I_p / I_s = N_s / N_pPrimary voltage divided by secondary voltage equals primary turns divided by secondary turns. Primary current divided by secondary current equals secondary turns divided by primary turns.

Real transformers have winding, core and stray losses, voltage regulation and thermal limits. Tap changers alter the effective ratio within an approved arrangement. Vector group records winding connection and phase displacement and is project-specific information. This introduction does not provide selection rules or protection settings.

11. Motors, generators and rotating equipment

Motors convert electrical energy to mechanical output; generators convert mechanical input to electrical output. Induction machines develop torque through relative motion between the rotating field and rotor. Synchronous machines operate at synchronous speed in steady state. Pole count and frequency determine the field speed.

n_s = 120f / p   ·   s = (n_s − n_r) / n_s × 100%Synchronous speed in revolutions per minute equals 120 multiplied by frequency divided by pole count. Percentage slip equals synchronous speed minus rotor speed, divided by synchronous speed, multiplied by one hundred.

Starting current, direction of rotation, driven-equipment condition and control method require project-specific checks. Mechanical power relates torque and angular speed through P = τω.

Worked example: At 50 Hz with four poles, synchronous speed is 120 × 50 ÷ 4 = 1,500 r/min. If measured rotor speed is 1,460 r/min, slip is (1,500 − 1,460) ÷ 1,500 × 100 = 2.67%.

For the overlapping mechanical relationship, open the Tools-owned torque, power and rotational-speed calculator.

12. Electrical distribution architecture

Electrical distribution connects sources to loads through controlled conversion, switching, protection and monitoring. Voltage labels such as high voltage (HV), medium voltage (MV) and low voltage (LV) vary by standard and jurisdiction; project definitions govern.

The same functional relationships appear across industrial, marine, offshore and critical-infrastructure projects, but the architecture, redundancy and authority model remain project-specific.

13. Protection, isolation, earthing and bonding

TN, TT and IT are high-level earthing-arrangement families. Their application, disconnection conditions and verification are jurisdiction- and project-specific. Breaking capacity is the fault current a device can interrupt under stated conditions. Selectivity or discrimination aims to have the appropriate device operate while retaining unaffected supply. Protection settings, time-current coordination and fault-level studies require approved engineering inputs; this page does not calculate or specify them.

14. Electrical inspection, testing and commissioning

A controlled progression establishes what is safe to inspect, what can be tested dead, what evidence is needed before energisation, and how the final configuration is confirmed. The approved project procedure, OEM requirements, specified test voltage, safety rules and authorised switching programme govern throughout.

1. Confirm approved documentation, test boundaries, responsibilities and acceptance criteria.
2. Verify equipment identity, nameplates, installation condition and mechanical completion.
3. Complete visual and mechanical inspection, including torque or termination evidence where specified.
4. Perform protective-conductor continuity, insulation-resistance, earthing, polarity and phase-sequence tests where applicable.
5. Complete cable tests appropriate to cable type and voltage, using approved methods and test values.
6. Complete transformer and motor checks against OEM and project requirements.
7. Test relays and protection, breaker function and trip paths, with controlled approved settings.
8. Verify controls, alarms, interlocks, meters and transducers, including scaling and interfaces.
9. Conduct an energisation-readiness review and obtain the required permits and authorisations.
10. Undertake controlled energisation only under the authorised switching programme.
11. Complete no-load and loaded functional tests within the approved envelope.
12. Verify transfer, failure modes and integration with control, monitoring and emergency systems.
13. Record the as-left configuration, restored protections, temporary arrangements and residual actions.

15. Records, acceptance and handover

Acceptance requires a traceable relationship between design intent, installed condition, test evidence, controlled exceptions and the receiving authority. The minimum record set is project-specific but commonly connects:

• approved single-line diagrams and load schedules
• cable schedules and equipment data sheets
• protection studies and approved settings
• FAT, SAT and installation-inspection records
• calibration certificates and test-equipment records
• cable, transformer, motor and equipment test results
• relay and breaker test reports
• energisation certificates, permits and switching records
• functional tests, trends, alarm and interlock matrices
• punch-list status and accepted deviations
• redlines, as-built drawings and as-left configuration
• operating procedures, training and O&M manuals
• final dossiers, residual actions and formal acceptance

A missing, failed or superseded record must remain visible with status and ownership. Signature alone does not correct an unsupported result or reconcile the field condition.

Continue the readiness and turnover trail

• Systems Completion and Turnover
• Commissioning Readiness
• Safe Handover and Start-Up
• Commissioning and Engineering Reference
• Electrical Engineering category
• Technical Library — authoritative-source context
• Tools — calculators and interactive aids

Primary source status, access conditions and limitations are recorded in the project’s Electrical Engineering Fundamentals source/change register. Citing a standard does not make it contractually applicable or provide access to its protected text.