City & Guilds Electrical Installation (Level 3) Electrical Science and Principles Syllabus

Electrical Science and Principles syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electrical Science and Principles in City & Guilds Electrical Installation (Level 3), not a summary of it.

1. 1

   Fundamental Electrical Theory

   4 topics

   • Units and quantities
     • SI base and derived units
     • Multiples and submultiples
   • Ohm's Law and circuit calculations
     • Voltage, current and resistance relationships
     • Power, energy and the power triangle
   • Series, parallel and combination circuits
     • Total resistance calculations
     • Current and voltage distribution
   • Resistivity and conductor sizing
     • Effect of length, area and temperature
2. 2

   Magnetism and Electromagnetism

   3 topics

   • Magnetic fields and flux
     • Flux density and magnetic field strength
     • B-H curves and hysteresis
   • Electromagnetic induction
     • Faraday's and Lenz's laws
     • Self and mutual inductance
   • Application in machines and transformers
     • Force on a current-carrying conductor
     • Generation of EMF
3. 3

   Alternating Current Theory

   4 topics

   • AC waveforms and quantities
     • Frequency, period and phase
     • Peak, RMS and average values
   • Reactance and impedance
     • Inductive and capacitive reactance
     • Impedance triangle
   • Power factor
     • True, apparent and reactive power
     • Causes and correction of low power factor
   • Resonance in series and parallel circuits
4. 4

   Three-Phase Systems

   4 topics

   • Three-phase generation and supply
     • Phase sequence and rotation
     • Line and phase relationships
   • Star and delta connections
     • Voltage and current relationships in star
     • Voltage and current relationships in delta
   • Balanced and unbalanced loads
     • Neutral current in unbalanced systems
   • Three-phase power calculations
5. 5

   Electrical Machines and Components

   4 topics

   • Transformers
     • Construction and operating principle
     • Turns ratio and voltage transformation
     • Losses and efficiency
   • AC motors
     • Three-phase induction motor principles
     • Slip and synchronous speed
     • Single-phase motor starting methods
   • DC machines and generators
   • Capacitors, inductors and resistors in service

Electrical Science and Principles flashcards for City & Guilds Electrical Installation (Level 3)

20 of 63 cards from the Electrical Science and Principles deck — real questions with worked answers.

1. State the seven SI base quantities and their units used in electrical science.

   Length — metre ($\text{m}$); mass — kilogram ($\text{kg}$); time — second ($\text{s}$); electric current — ampere ($\text{A}$); thermodynamic temperature — kelvin ($\text{K}$); amount of substance — mole ($\text{mol}$); luminous intensity — candela ($\text{cd}$).

2. Define the coulomb and relate charge, current and time.

   One coulomb is the charge transported by a current of $1\,\text{A}$ in $1\,\text{s}$. The relationship is $Q = I \times t$, where $Q$ is in coulombs, $I$ in amperes and $t$ in seconds.

3. What do the SI prefixes milli, micro, kilo and mega represent as powers of ten?

   milli $= 10^{-3}$, micro $= 10^{-6}$, kilo $= 10^{3}$, mega $= 10^{6}$.

4. Define the volt in terms of energy and charge.

   One volt is the potential difference that converts $1\,\text{J}$ of energy per coulomb of charge: $V = \dfrac{W}{Q}$, where $W$ is energy in joules and $Q$ is charge in coulombs.

5. State Ohm's Law and its three rearranged forms.

   Ohm's Law: the current through a conductor is proportional to the voltage across it at constant temperature. $V = IR$, $I = \dfrac{V}{R}$, $R = \dfrac{V}{I}$.

6. Give the three formulas for electrical power in a DC resistive circuit.

   $P = VI$, $P = I^{2}R$, and $P = \dfrac{V^{2}}{R}$, where $P$ is in watts.

7. How is electrical energy calculated and what is the unit used for billing?

   Energy $W = P \times t$. In SI it is measured in joules ($\text{J}$); for billing the kilowatt-hour ($\text{kWh}$) is used, where $1\,\text{kWh} = 3.6 \times 10^{6}\,\text{J}$.

8. For resistors in series, how do you find total resistance and what is shared between them?

   Total resistance is the sum: $R_{T} = R_{1} + R_{2} + R_{3} + \dots$. The same current flows through all resistors; the supply voltage divides across them.

9. For resistors in parallel, give the general formula and the two-resistor shortcut.

   $\dfrac{1}{R_{T}} = \dfrac{1}{R_{1}} + \dfrac{1}{R_{2}} + \dots$. For two resistors: $R_{T} = \dfrac{R_{1}R_{2}}{R_{1}+R_{2}}$. The voltage is common; current divides.

10. State the voltage divider rule for two series resistors $R_1$ and $R_2$ across supply $V$.

    The voltage across $R_{1}$ is $V_{1} = V \times \dfrac{R_{1}}{R_{1}+R_{2}}$.

11. How do you analyse a combination (series–parallel) circuit?

    Reduce parallel groups to a single equivalent resistance first, then add series resistances to find total $R_{T}$. Use $I = V/R_{T}$ for total current, then work back to find branch voltages and currents using Ohm's Law and the divider rules.

12. State Kirchhoff's current and voltage laws.

    Current law (KCL): the sum of currents entering a junction equals the sum leaving it ($\sum I = 0$). Voltage law (KVL): around any closed loop the sum of EMFs equals the sum of voltage drops ($\sum V = 0$).

13. Write the resistivity formula and define each term with units.

    $R = \dfrac{\rho l}{A}$, where $R$ = resistance ($\Omega$), $\rho$ = resistivity ($\Omega\,\text{m}$), $l$ = length ($\text{m}$) and $A$ = cross-sectional area ($\text{m}^{2}$).

14. How does conductor resistance change with length and cross-sectional area?

    Resistance is directly proportional to length and inversely proportional to cross-sectional area: doubling the length doubles $R$; doubling the area halves $R$.

15. How does the resistance of a metallic conductor vary with temperature, and what is the governing equation?

    For metals resistance increases with temperature (positive temperature coefficient). $R_{2} = R_{1}\left[1 + \alpha(\theta_{2} - \theta_{1})\right]$, where $\alpha$ is the temperature coefficient of resistance per $^{\circ}\text{C}$.

16. Why is copper preferred over aluminium for many conductors, and one advantage of aluminium?

    Copper has lower resistivity ($\approx 1.7 \times 10^{-8}\,\Omega\,\text{m}$) so smaller cross-section for a given current, and good mechanical/jointing properties. Aluminium ($\approx 2.8 \times 10^{-8}\,\Omega\,\text{m}$) is lighter and cheaper, used for overhead lines and large feeders.

17. Define magnetic flux and magnetic flux density, with their units.

    Magnetic flux $\Phi$ is the total magnetic field, measured in webers ($\text{Wb}$). Flux density $B = \dfrac{\Phi}{A}$ is flux per unit area, measured in teslas ($\text{T}$), where $1\,\text{T} = 1\,\text{Wb/m}^{2}$.

18. Define magnetomotive force (MMF) and magnetic field strength $H$.

    MMF $= NI$ (ampere-turns), the magnetic 'driving force' of a coil. Magnetic field strength $H = \dfrac{NI}{l}$ in $\text{A/m}$, where $l$ is the magnetic path length.

19. What is permeability and how are $B$ and $H$ related?

    Permeability is the ease with which a material carries flux: $B = \mu H = \mu_{0}\mu_{r}H$, where $\mu_{0} = 4\pi \times 10^{-7}\,\text{H/m}$ is the permeability of free space and $\mu_{r}$ is the relative permeability of the material.

20. State Faraday's law of electromagnetic induction.

    The induced EMF is proportional to the rate of change of magnetic flux linkage: $e = -N\dfrac{d\Phi}{dt}$, where $N$ is the number of turns.

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