Journeyman/Master Electrician License Exam Electrical Theory and Fundamentals Syllabus

Electrical Theory and Fundamentals syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electrical Theory and Fundamentals in Journeyman/Master Electrician License Exam, not a summary of it.

1. 1

   Basic Electrical Quantities and Laws

   4 topics

   • Voltage, Current, Resistance, and Power
     • Definitions and units (volt, ampere, ohm, watt)
     • Conductors, insulators, and semiconductors
     • Conventional current vs. electron flow
   • Ohm's Law and the Power Wheel
     • E = I x R rearrangements
     • P = I x E and P = I^2 x R derivations
     • Applying the 12-formula power wheel
   • Series, Parallel, and Combination Circuits
     • Total resistance in series and parallel networks
     • Voltage division and current division
     • Kirchhoff's voltage and current laws
   • Energy, Work, and Cost Calculations
     • Kilowatt-hour computation
     • Demand vs. energy billing concepts
2. 2

   Alternating Current Principles

   4 topics

   • AC Waveforms and Values
     • Peak, RMS, and average values
     • Frequency, period, and phase angle
   • Inductance, Capacitance, and Reactance
     • Inductive and capacitive reactance (XL, XC)
     • Impedance and the impedance triangle
   • Power Factor and the Power Triangle
     • True, reactive, and apparent power (W, VAR, VA)
     • Power factor correction with capacitors
   • Single-Phase vs. Three-Phase Systems
     • Wye and delta configurations
     • Line vs. phase voltage and current relationships (1.732 factor)
3. 3

   Magnetism and Electromagnetic Devices

   3 topics

   • Magnetism and Electromagnetic Induction
     • Faraday's and Lenz's laws
     • Left-hand and right-hand rules
   • Transformers
     • Turns ratio and voltage/current transformation
     • Step-up, step-down, and autotransformers
     • kVA sizing and transformer connections
   • Motors and Generators
     • AC induction motor operation and slip
     • Synchronous speed and horsepower-to-watt conversion
     • Motor starting methods and torque

Electrical Theory and Fundamentals flashcards for Journeyman/Master Electrician License Exam

24 of 50 cards from the Electrical Theory and Fundamentals deck — real questions with worked answers.

1. Define voltage (electromotive force) and state its unit and symbol.

   Voltage is the electrical potential difference, or "pressure," that drives current through a circuit. It is the work done per unit charge: $V = \frac{W}{Q}$. Unit: the volt $(\text{V})$; one volt equals one joule per coulomb $\left(1\,\text{V} = 1\,\frac{\text{J}}{\text{C}}\right)$.

2. Define electric current and state its unit and the relationship to charge and time.

   Current is the rate of flow of electric charge. $I = \frac{Q}{t}$, where $Q$ is charge in coulombs and $t$ is time in seconds. Unit: the ampere $(\text{A})$; one ampere equals one coulomb per second $\left(1\,\text{A} = 1\,\frac{\text{C}}{\text{s}}\right)$.

3. Define resistance, state its unit, and name the factors that affect a conductor's resistance.

   Resistance is opposition to current flow, measured in ohms $(\Omega)$. For a conductor, $R = \frac{\rho L}{A}$, so resistance increases with resistivity $\rho$ and length $L$, and decreases with cross-sectional area $A$. It also rises with temperature for most metals.

4. State Ohm's Law in its three algebraic forms.

   $$V = I \times R, \qquad I = \frac{V}{R}, \qquad R = \frac{V}{I}$$ where $V$ is volts, $I$ is amperes, and $R$ is ohms.

5. State the three basic power formulas relating power, voltage, and current.

   $$P = V \times I, \qquad P = I^{2} \times R, \qquad P = \frac{V^{2}}{R}$$ Power $P$ is in watts $(\text{W})$.

6. Using the Power Wheel, how do you find current when only power and resistance are known?

   $$I = \sqrt{\frac{P}{R}}$$ derived from $P = I^{2}R$.

7. Using the Power Wheel, how do you find voltage when only power and resistance are known?

   $$V = \sqrt{P \times R}$$ derived from $P = \frac{V^{2}}{R}$.

8. In a series circuit, how do total resistance, current, and voltage behave?

   Resistances add: $R_T = R_1 + R_2 + \cdots + R_n$. Current is the same through every component: $I_T = I_1 = I_2$. Voltage divides across components and sums to the source: $V_T = V_1 + V_2 + \cdots + V_n$.

9. In a parallel circuit, how do total resistance, voltage, and current behave?

   Voltage is the same across every branch: $V_T = V_1 = V_2$. Branch currents add: $I_T = I_1 + I_2 + \cdots$. Total resistance is found from $$\frac{1}{R_T} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}$$ and is always less than the smallest branch resistance.

10. Give the shortcut formula for the total resistance of exactly two resistors in parallel.

    $$R_T = \frac{R_1 \times R_2}{R_1 + R_2}$$ (the "product over sum" method).

11. What is the total resistance of $n$ equal resistors of value $R$ connected in parallel?

    $$R_T = \frac{R}{n}$$ For example, four $100\,\Omega$ resistors in parallel give $25\,\Omega$.

12. Describe the general process for solving a combination (series-parallel) circuit.

    1) Reduce parallel groups to single equivalent resistances. 2) Add those in series with any series resistors to find $R_T$. 3) Find total current with $I_T = \frac{V_T}{R_T}$. 4) Work back outward applying Ohm's Law and the series/parallel rules to find individual voltages and currents.

13. State Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL).

    KVL: the algebraic sum of all voltages around any closed loop equals zero ($\sum V = 0$); voltage drops equal the applied voltage. KCL: the algebraic sum of currents entering a node equals the sum leaving it ($\sum I_{in} = \sum I_{out}$).

14. Define electrical energy/work and give the formula used for billing.

    Electrical energy (work) is power consumed over time: $W = P \times t$. For billing, energy is measured in kilowatt-hours: $$\text{kWh} = \frac{P_{(\text{watts})} \times t_{(\text{hours})}}{1000}$$

15. How do you calculate the operating cost of an electrical load?

    $$\text{Cost} = \text{kWh} \times \text{rate} = \frac{P_{(\text{W})} \times t_{(\text{h})}}{1000} \times (\text{\$/kWh})$$ Multiply energy used in kWh by the utility's price per kilowatt-hour.

16. A $1500\,\text{W}$ heater runs $4$ hours per day at \$0.12/kWh. What is the daily cost?

    Energy $= \frac{1500 \times 4}{1000} = 6\,\text{kWh}$. Cost $= 6 \times \$0.12 = \$0.72$ per day.

17. Define one joule of work in electrical terms.

    One joule is the energy transferred when one coulomb of charge moves through a potential difference of one volt, equivalently one watt acting for one second: $1\,\text{J} = 1\,\text{W}\cdot\text{s} = 1\,\text{V}\cdot\text{C}$.

18. Define one cycle, period, and frequency of an AC waveform.

    A cycle is one complete positive-and-negative alternation of the waveform. The period $T$ is the time for one cycle (seconds). Frequency $f$ is cycles per second (hertz). They are reciprocals: $$f = \frac{1}{T}, \qquad T = \frac{1}{f}$$ Standard US power is $60\,\text{Hz}$.

19. For a sine wave, define peak, peak-to-peak, and how RMS relates to peak voltage.

    Peak ($V_p$) is the maximum value from zero. Peak-to-peak is $V_{pp} = 2 V_p$. RMS (effective) value: $$V_{rms} = \frac{V_p}{\sqrt{2}} = 0.707\,V_p, \qquad V_p = 1.414\,V_{rms}$$

20. What is the average value of a sine wave over a half-cycle, and why is RMS used instead?

    Average over a half-cycle is $V_{avg} = 0.637\,V_p$. RMS (root-mean-square) is used for power because $V_{rms} = 0.707\,V_p$ represents the equivalent DC value that produces the same heating effect in a resistance.

21. If a US outlet reads $120\,\text{V}$ RMS, what are its peak and peak-to-peak voltages?

    $V_p = 120 \times 1.414 \approx 169.7\,\text{V}$. $V_{pp} = 2 \times 169.7 \approx 339.4\,\text{V}$.

22. Define inductance, state its unit, and describe how an inductor opposes change.

    Inductance is the property of a coil that opposes a change in current by inducing a counter-EMF. Unit: the henry $(\text{H})$. The induced voltage is $$v_L = L \frac{di}{dt}$$ In an inductor, current lags voltage by $90^{\circ}$.

23. Define capacitance, state its unit, and describe the charge relationship.

    Capacitance is the ability to store charge in an electric field between two plates. Unit: the farad $(\text{F})$. Charge stored: $Q = C \times V$. In a capacitor, current leads voltage by $90^{\circ}$.

24. Give the formulas for inductive reactance and capacitive reactance.

    $$X_L = 2\pi f L, \qquad X_C = \frac{1}{2\pi f C}$$ Both are measured in ohms $(\Omega)$. $X_L$ rises with frequency; $X_C$ falls with frequency.

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