Electrical Engineering Foundations, Quantities and Safety

Introduction

Electrical engineering begins with a small set of physical quantities and conventions that describe how electric charge is stored, moved, and converted into useful effects. These foundations are essential in mechatronics, where electrical circuits interact with mechanical systems, sensors, actuators, controllers, and computer-based automation.

A mechatronics engineer must do more than calculate circuit values. They must select appropriate sources and components, interpret measurements, recognize hazards, isolate energy safely, document work accurately, and make decisions consistent with professional ethics. This chapter develops that foundation.

Learning Objectives

By the end of this chapter, you should be able to:

1. Define electric charge, current, voltage, power, energy, resistance, and conductance.
2. Use SI units and engineering prefixes correctly.
3. Distinguish voltage sources, current sources, and practical sources.
4. Apply Ohm’s law and power relationships under stated assumptions.
5. Use the passive sign convention to determine whether a component absorbs or delivers power.
6. Explain electrical hazards, protective measures, isolation procedures, and safe laboratory practice.
7. Apply ethical and professional responsibilities when designing, testing, and reporting electrical systems.

1. Electric Charge and Matter

Electric charge is a fundamental property of matter. It exists in two types, conventionally called positive and negative. Protons carry positive charge, electrons carry negative charge, and neutrons have no net charge. The SI unit of charge is the coulomb (C). The magnitude of the charge of one electron is approximately 1.602 × 10^-19 C.

Charge is quantized: the net charge of an isolated body is an integral multiple of the elementary charge. In ordinary circuit analysis, however, charge is treated as a continuous variable because the number of charge carriers is extremely large.

Conductors, such as copper and aluminium, contain mobile electrons. Insulators, such as glass and many plastics, strongly restrict charge movement. Semiconductor materials have electrical behavior that can be controlled through composition, temperature, light, and applied voltage.

Charge is conserved. It is not created or destroyed in an electrical circuit, although it can move between locations and electrical energy can be transformed into heat, light, motion, or stored field energy.

2. Electric Current

Electric current is the rate at which charge passes a specified cross-section:

Here, I is current in amperes (A), q is charge in coulombs, and t is time in seconds. One ampere is one coulomb per second. For a constant current:

Conventional current is defined as the direction in which positive charge would move. In metallic conductors, electrons actually move in the opposite direction. Circuit theory uses conventional current because it provides a consistent sign convention for all circuit elements.

A current may be direct or alternating. Direct current (DC) maintains a constant direction, although its magnitude may vary. Alternating current (AC) reverses direction periodically. Batteries and regulated supplies commonly provide DC; utility distribution systems commonly provide AC.

Current cannot exist continuously through a complete circuit unless a conducting path is available. An open switch ideally has zero current through it, while an ideal short circuit has zero voltage across it. Real switches and conductors have small but nonzero resistance.

3. Voltage and Electrical Potential Energy

Voltage is the energy transferred per unit charge between two points. The voltage from point a to point b is defined as:

where v_ab is voltage in volts (V), w is energy or work in joules (J), and q is charge in coulombs. One volt equals one joule per coulomb.

Voltage is always a difference between two points; there is no meaningful voltage at a single isolated point without a reference. A circuit node may be assigned zero volts as a reference, often called ground, but this does not necessarily mean that the node is physically connected to Earth.

A voltage source supplies a specified potential difference. When a positive terminal is labelled relative to a negative terminal, a positive test charge would gain or lose energy according to the source and the direction of movement. Voltage itself is not a flow quantity: current flows, while voltage exists between points.

4. Power and Energy

Electrical power is the rate of energy transfer:

where p is power in watts (W), w is energy in joules, and t is time in seconds. Combining the definitions of voltage and current gives the instantaneous circuit relationship:

This equation applies when the voltage and current use a consistent reference direction and polarity. The unit is watt because 1 W = 1 J/s.

Energy transferred over an interval is:

For constant power:

Energy is measured in joules in the SI system. Electrical energy supplied to consumers is often recorded in kilowatt-hours (kWh):

Power may be absorbed or delivered. A motor absorbs electrical power and converts much of it into mechanical power, while a generator delivers electrical power by converting mechanical or other energy into electrical form. Some power is inevitably lost as heat because practical conductors and components have resistance.

Worked Example 1: Energy Consumption

A 60 W lamp operates for 5 h. Its energy consumption is:

In joules:

The calculation assumes that the lamp consumes constant power.

5. Resistance and Ohm’s Law

Resistance describes opposition to current. The SI unit is the ohm (Ω). For an ohmic component operating under constant physical conditions, Ohm’s law is:

where v is voltage in volts, i is current in amperes, and R is resistance in ohms. The relationship may also be written as:

or

Ohm’s law is not a universal law for every electrical device. It applies to a component or operating region in which voltage is proportional to current. A fixed resistor approximately satisfies this condition over its rated temperature and power range. Diodes, transistors, lamps, batteries, and many sensors are nonlinear and require a more complete voltage–current characteristic.

For a uniform wire, resistance depends on material, length, and cross-sectional area:

Here, ρ is resistivity in Ω·m, ℓ is conductor length in metres, and A is cross-sectional area in square metres. The equation assumes approximately uniform material and temperature. Since resistivity usually changes with temperature, resistance also changes with temperature.

Power in a Resistor

Substitution of Ohm’s law into p = vi gives, for a resistive element:

These forms are valid for a resistor and consistent voltage-current references. They show that increasing current can greatly increase heating because power varies with the square of current.

Worked Example 2: Resistor Current and Power

A 12 V supply is connected to a 6 Ω resistor. Assuming an ideal DC source and an ohmic resistor:

The absorbed power is:

Equivalently, p = i²R = (2 A)² × 6 Ω = 24 W. The resistor must be selected with a suitable power rating, normally with a safety margin above 24 W.

6. SI Units and Engineering Prefixes

Consistent units prevent design and measurement errors. Important electrical units include:

Common prefixes are kilo (k, 10³), mega (M, 10⁶), giga (G, 10⁹), milli (m, 10^-3), micro (μ, 10^-6), and nano (n, 10^-9). Case matters: mW means milliwatt, whereas MW means megawatt.

A value should be converted into consistent units before substitution. For example, 2.5 mA is 2.5 × 10^-3 A, not 2.5 A.

7. Sources and Circuit Models

A source is an element capable of supplying electrical energy. Two ideal source models are fundamental.

Voltage Source

An ideal voltage source maintains a prescribed voltage independent of its current. An ideal voltage source may deliver any current required by the connected circuit, which is physically impossible in unlimited form. A practical voltage source is modelled by an ideal voltage source in series with internal resistance.

If a source has open-circuit voltage V_s and internal resistance R_s, the terminal voltage under load current I is approximately:

The equation assumes current leaves the positive terminal and the internal resistance is constant.

Current Source

An ideal current source maintains a prescribed current independent of its terminal voltage. A practical current source is commonly represented by an ideal current source in parallel with internal resistance. Neither ideal model should be interpreted as a complete physical description; models are useful within their intended operating range.

Sources may also be independent or dependent. An independent source has a specified value. A dependent source is controlled by another voltage or current in the circuit and is useful for modelling amplifiers, transistors, and feedback systems.

8. Passive Sign Convention

The passive sign convention defines the reference polarity and current direction so that current enters the terminal marked positive. Under this convention:

If p > 0, the element absorbs power. If p < 0, the element delivers power according to the selected references. This is a bookkeeping convention, not a claim that a component is inherently passive or active.

For example, a resistor always absorbs power in normal operation because its voltage and current references produce a positive value. A battery being charged absorbs power; the same battery discharging delivers power, and the signs change accordingly.

The conservation principle for an interconnected circuit is:

The algebraic sum of power absorbed and delivered by all elements is zero, assuming no unmodelled energy path. This is a powerful check on calculations.

9. Electrical Hazards

Electrical hazards arise from energy, not merely from voltage labels. Important hazards include:

• Electric shock: current passing through the body can cause pain, involuntary muscular contraction, respiratory failure, burns, or cardiac disturbance.
• Arc flash and arc blast: an unintended electrical arc can produce intense heat, molten metal, pressure, ultraviolet radiation, and toxic fumes.
• Thermal fire: overloaded conductors, poor connections, and incorrectly rated components can overheat.
• Stored energy: capacitors, inductors, batteries, and elevated mechanical systems may remain hazardous after a source is disconnected.
• Unexpected motion: motors, pneumatic systems, robots, and actuators may move when power is restored or a control signal changes.
• Measurement hazards: incorrect meter connections can create short circuits or expose the user to hazardous potential.

Risk depends on voltage, available current, source impedance, contact duration, body path, environment, and skin condition. Moisture lowers body resistance and increases risk. Even low-voltage systems can cause burns, fire, or dangerous motion.

10. Laboratory Safety and Isolation

Safety begins before energization. A professional procedure includes the following sequence:

1. Identify all electrical, mechanical, pneumatic, hydraulic, thermal, chemical, and stored-energy hazards.
2. Consult the circuit diagram, equipment manual, risk assessment, and applicable laboratory rules.
3. De-energize the system whenever possible.
4. Isolate every energy source, including mains supply, batteries, capacitors, auxiliary supplies, and remote-control paths.
5. Lock and tag isolation points where the procedure requires it.
6. Test the measuring instrument on a known live source, test the isolated circuit, and retest the instrument on the known live source. This verifies that the instrument functions correctly.
7. Discharge capacitors through an approved method and verify zero energy using an appropriate instrument.
8. Protect against re-energization and unexpected mechanical movement.
9. Use suitable insulated tools, personal protective equipment, barriers, and current-limited supplies.
10. Energize only after all personnel are clear and the test plan is understood.

A fuse or circuit breaker protects equipment and conductors; it does not make all contact with a live circuit safe. Grounding, protective bonding, residual-current protection, insulation, enclosures, and separation are complementary controls.

Never rely on a schematic alone as proof of isolation. Wires may be mislabelled, back-fed, or connected to a second source. Never use a current-mode multimeter across a voltage source because the meter can behave nearly as a short circuit and cause a high fault current.

11. Safe Measurement Practice

A voltmeter is connected in parallel because it measures potential difference between two points and is designed with high input resistance. An ammeter is connected in series because the circuit current must pass through it; it is designed with low resistance. An ohmmeter must be used only on a de-energized circuit because it applies its own test signal.

Before measuring, check:

• expected voltage and current levels;
• meter category and maximum rating;
• lead condition and terminal selection;
• probe insulation and protective equipment;
• whether the circuit contains transients or stored energy;
• whether the selected range is appropriate.

A measurement is not automatically correct because a number appears on a display. The engineer must assess whether the reading is physically plausible, whether the instrument was connected correctly, and whether loading or grounding affected the circuit.

12. Illustrative Case: Unexpected Motion in a Mechatronics Laboratory

Background. A student team is testing a 24 V motor-driven linear actuator controlled by a microcontroller. The actuator has a separate motor supply and a USB-connected programming computer.

Problem. The team switches off the motor supply and begins adjusting the mechanism. The actuator suddenly moves when a control cable is reconnected.

Analysis. The motor supply was off, but the controller remained powered through the USB connection. A control output changed state during reconnection, and the motor driver received enough power through an auxiliary path to activate briefly. The team had isolated one source but not all energy paths.

Approach. The team revises its procedure: disconnect the motor supply and USB supply, remove the actuator’s stored mechanical load where possible, apply a lockout label, support the moving mechanism, and verify absence of voltage at the driver terminals. A current-limited bench supply and a physical emergency-stop circuit are added for testing. The control program is changed so that outputs initialize to a safe state.

Outcome. Unexpected motion is eliminated during adjustment, and the revised test procedure is documented for future users. The incident is reported without blaming an individual, allowing the laboratory to improve its design and training.

Learning points. Isolation must include every source and back-feed path. Software defaults are part of safety design but do not replace physical isolation. Mechanical energy and control energy must be considered alongside electrical supply energy. Reporting near misses is an ethical engineering practice because it prevents recurrence.

13. Ethics, Responsibility, and Professional Practice

Electrical engineers have a duty to protect people, property, and the environment. This duty includes designing within competence, following applicable standards and institutional procedures, identifying hazards honestly, and communicating uncertainty.

Engineers should never conceal failed tests, falsify measurements, bypass protective devices for convenience, or approve equipment they have not adequately inspected. Technical records should identify assumptions, instrument limitations, calibration status, test conditions, and deviations from the intended design.

Safety requirements should be treated as design requirements rather than paperwork added at the end. A responsible design uses inherently safer voltages where practical, limits fault energy, provides accessible isolation, prevents incorrect connections, and considers maintenance and end-of-life disposal.

Standards and regulations vary by jurisdiction and application. Laboratory users must follow the requirements adopted by their institution and local authorities. This chapter presents general principles, not a substitute for formal electrical-safety training or legally applicable codes.

14. Contemporary Engineering Practice

Modern mechatronic systems combine power electronics, embedded controllers, wireless communication, batteries, and cloud-connected monitoring. These technologies introduce new safety concerns: lithium battery thermal runaway, regenerative energy from drives, electromagnetic interference, remote commands, and cyber-physical faults.

Engineering teams increasingly use digital simulation, automated test equipment, data logging, and AI-assisted design tools. Such tools can identify patterns and accelerate analysis, but their outputs require engineering verification. An AI-generated circuit, code fragment, or safety claim must be checked against physical laws, ratings, standards, and test evidence. Responsibility cannot be delegated to software.

Best practice is therefore a combination of sound theory, conservative design margins, controlled experiments, peer review, traceable documentation, and continuous learning.

Chapter Summary

Electric charge is conserved and is measured in coulombs. Current is the rate of charge flow, while voltage is energy transferred per unit charge. Power is the rate of energy transfer and, with consistent references, is calculated from p = vi. Energy is the integral of power over time. Resistance relates voltage and current in an ohmic operating region through Ohm’s law, and resistor power may be written as p = i²R or p = v²/R.

Ideal voltage and current sources are useful models, but practical sources have internal limitations. The passive sign convention makes positive power indicate absorption and negative power indicate delivery. Unit consistency, dimensional reasoning, and power conservation provide essential calculation checks.

Electrical safety requires hazard identification, complete isolation, verification of de-energization, control of stored energy, suitable instruments, and prevention of unexpected motion. Ethical practice requires honest records, respect for standards, reporting of near misses, and recognition that engineers remain responsible for decisions made with software or AI assistance.

Key Terms

Charge: A physical property of matter measured in coulombs.

Current: Rate of charge flow, measured in amperes.

Voltage: Energy transferred per unit charge between two points.

Power: Rate of energy transfer, measured in watts.

Energy: Capacity to perform work; electrically measured in joules or kilowatt-hours.

Resistance: Opposition to current, measured in ohms.

Resistivity: Material property used to calculate the resistance of a uniform conductor.

Ohm’s law: The relationship v = iR for an ohmic element.

Conductance: Reciprocal of resistance, measured in siemens.

Voltage source: Circuit element intended to maintain a specified voltage.

Current source: Circuit element intended to maintain a specified current.

Internal resistance: Resistance included in a practical source model.

Passive sign convention: Reference convention in which current enters the positive voltage terminal.

Ground: A selected reference node or protective connection, depending on context.

Isolation: Separation of equipment from all hazardous energy sources.

Stored energy: Energy remaining in capacitors, inductors, batteries, or mechanical systems after disconnection.

Arc flash: Hazardous release of heat, light, pressure, and molten material from an electrical arc.

Lockout/tagout: A controlled method of preventing re-energization during work.

Near miss: An incident that could have caused harm but did not.

Review Questions

Short Answer Questions

1. Define electric current and state its SI unit.
2. Why is voltage described as a difference between two points?
3. State the passive sign convention and explain the meaning of positive power.
4. Distinguish an ideal voltage source from a practical voltage source.
5. Why must an ohmmeter be used only on a de-energized circuit?

Long Answer Questions

1. Explain the relationships among charge, current, voltage, power, and energy, including their units and principal equations.
2. Discuss Ohm’s law, its assumptions, and why it cannot be applied indiscriminately to nonlinear devices.
3. Explain how voltage and current sources are modelled in practical circuits and identify limitations of ideal models.
4. Describe a complete laboratory isolation and verification procedure for a mechatronic system.
5. Discuss the ethical responsibilities of an engineer who discovers an unsafe design or an inaccurate test record.

Analytical / Application Questions

1. A 24 V source supplies a 12 Ω resistor. Calculate the current and resistor power, then state a suitable design consideration for selecting the resistor rating.
2. A practical 12 V source has an internal resistance of 0.50 Ω and supplies a load current of 2 A. Calculate its approximate terminal voltage and explain why it differs from the open-circuit voltage.
3. Design a safe test plan for a motorized actuator with a mains-powered supply, a battery backup, a capacitor bank, and a computer control connection. Identify isolation points, verification steps, stored-energy hazards, and controls against unexpected motion.

Multiple Choice Questions with Answers

Question 1

Which quantity is defined as the rate of charge flow?

A. Voltage

B. Current

C. Power

D. Resistance

Correct Answer: B. Current

Question 2

A 10 Ω resistor is connected to an ideal 20 V DC source. What current flows?

A. 0.5 A

B. 2 A

C. 10 A

D. 200 A

Correct Answer: B. 2 A

Question 3

Under the passive sign convention, positive power means that an element is:

A. Delivering power

B. Absorbing power

C. Disconnected

D. At zero voltage

Correct Answer: B. Absorbing power

Question 4

Which unit is equivalent to one joule per coulomb?

A. Ampere

B. Ohm

C. Volt

D. Watt

Correct Answer: C. Volt

Question 5

What is the correct relationship for the power absorbed by a resistor?

A. p = iR

B. p = v + i

C. p = i²R

D. p = R/i

Correct Answer: C. p = i²R

Question 6

Why is a voltmeter connected in parallel?

A. It has intentionally low resistance

B. It measures current through a component

C. It measures potential difference between two points

D. It replaces the circuit source

Correct Answer: C. It measures potential difference between two points

Question 7

Which action best verifies that an isolation test instrument is functioning?

A. Test only the isolated circuit

B. Test a known live source before and after testing the isolated circuit

C. Touch the probes together at mains voltage

D. Assume the display is accurate

Correct Answer: B. Test a known live source before and after testing the isolated circuit

Question 8

A 60 W device operates for 2 hours. How much energy does it consume?

A. 0.03 kWh

B. 0.12 kWh

C. 30 kWh

D. 120 kWh

Correct Answer: B. 0.12 kWh

Question 9

Which statement about an ideal current source is correct?

A. It maintains prescribed current independent of terminal voltage

B. It always has zero terminal voltage

C. It can supply no power

D. It must be connected in series with every load

Correct Answer: A. It maintains prescribed current independent of terminal voltage

Question 10

Why should an engineer report a laboratory near miss?

A. To assign blame automatically

B. To avoid documenting procedures

C. To enable corrective action and prevent recurrence

D. To prove that no hazard existed

Correct Answer: C. To enable corrective action and prevent recurrence