Journeyman/Master Electrician License Exam Electrical Theory and Fundamentals Syllabus

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

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

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 $90^{\circ}$.

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 $90^{\circ}$.

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.

Define impedance and give the formula for a series RLC-type circuit.

Impedance $Z$ is the total opposition to AC, combining resistance and reactance, measured in ohms. $$Z = \sqrt{R^{2} + (X_L - X_C)^{2}}$$ AC Ohm's Law: $V = I \times Z$.

Compare how inductors and capacitors phase-shift current relative to voltage. (Memory aid?)

Inductor: current lags voltage by $90^{\circ}$. Capacitor: current leads voltage by $90^{\circ}$. Memory aid "ELI the ICE man": in an inductor (L), E leads I (ELI); in a capacitor (C), I leads E (ICE).

Define power factor and give its formula.

Power factor is the ratio of real (true) power to apparent power, equal to the cosine of the phase angle: $$PF = \frac{P}{S} = \cos\theta$$ It ranges from $0$ to $1$ and is often expressed as a percentage; a purely resistive load has $PF = 1$.

Name the three quantities of the power triangle, their units, and their relationship.

Real (true) power $P$ in watts $(\text{W})$; reactive power $Q$ in volt-amperes reactive $(\text{VAR})$; apparent power $S$ in volt-amperes $(\text{VA})$. They relate as $$S = \sqrt{P^{2} + Q^{2}}, \qquad P = S\cos\theta, \qquad Q = S\sin\theta$$

A motor draws $10\,\text{kVA}$ apparent power with a power factor of $0.8$. What is the real power?

$P = S \times PF = 10\,\text{kVA} \times 0.8 = 8\,\text{kW}$.

Why is a low (poor) power factor undesirable for a facility?

A low power factor means more current is drawn for the same real power, causing larger $I^{2}R$ losses, voltage drop, oversized conductors/equipment, and utility penalty charges. It is commonly corrected by adding capacitors to offset inductive (lagging) reactive power.

Give the formula for apparent power in a single-phase and in a three-phase system.

Single-phase: $S = V \times I$. Three-phase: $$S = \sqrt{3} \times V_L \times I_L$$ where $V_L$ and $I_L$ are line voltage and line current.

In a three-phase wye (star) connection, how do line and phase voltages and currents relate?

Line voltage is $\sqrt{3}$ times phase voltage: $V_L = \sqrt{3}\,V_{ph}$. Line current equals phase current: $I_L = I_{ph}$. Example: $120\,\text{V}$ phase gives $120 \times 1.732 \approx 208\,\text{V}$ line.

In a three-phase delta connection, how do line and phase voltages and currents relate?

Line voltage equals phase voltage: $V_L = V_{ph}$. Line current is $\sqrt{3}$ times phase current: $I_L = \sqrt{3}\,I_{ph}$.

State two advantages of three-phase power over single-phase power.

Three-phase delivers constant, non-pulsating power and more power per conductor (greater efficiency and smaller conductors for the same load). It also allows self-starting motors with rotating magnetic fields and requires less conductor material than equivalent single-phase systems.

By how many electrical degrees are the three phases of a three-phase system separated?

The phases are separated by $120^{\circ}$ each, so the three sine waves are evenly spaced over the $360^{\circ}$ cycle ($3 \times 120^{\circ} = 360^{\circ}$).

State the formula for three-phase real (true) power.

$$P = \sqrt{3} \times V_L \times I_L \times \cos\theta$$ where $\cos\theta$ is the power factor, $V_L$ is line voltage, and $I_L$ is line current; result in watts.

State the law of magnetic poles and define magnetic flux.

Like magnetic poles repel; unlike poles attract. Magnetic flux $\Phi$ is the total number of magnetic field lines, measured in webers $(\text{Wb})$ (or maxwells/lines in the CGS system); flux density $B$ is flux per unit area, in teslas $(\text{T})$.

State Faraday's Law of electromagnetic induction.

The induced EMF in a coil is proportional to the rate of change of magnetic flux linking it: $$e = -N \frac{d\Phi}{dt}$$ where $N$ is the number of turns. Faster flux change or more turns produces greater induced voltage.

State Lenz's Law.

An induced current always flows in a direction such that its own magnetic field opposes the change in flux that produced it. This is the reason for the negative sign in Faraday's law and explains counter-EMF in inductors and motors.

What three conditions are required to induce a voltage by electromagnetic induction?

You need (1) a magnetic field, (2) a conductor, and (3) relative motion between them (or a changing magnetic field) so that the conductor cuts magnetic lines of force. No relative motion or flux change means no induced EMF.

Describe the left-hand rule for the magnetic field around a current-carrying conductor (electron flow).

Using electron-flow (conventional left-hand) convention: grasp the conductor with the left hand so the thumb points in the direction of electron current; the curled fingers point in the direction of the circular magnetic field around the conductor.

What is the purpose of a transformer, and can it change power levels?

A transformer transfers AC energy between circuits via mutual induction, stepping voltage up or down (and current inversely). It cannot create power; ideally output power equals input power: $P_{pri} \approx P_{sec}$. It does not work on steady DC.

State the transformer turns ratio relationship for voltage and current.

$$\frac{V_p}{V_s} = \frac{N_p}{N_s} = \frac{I_s}{I_p}$$ Voltage is proportional to turns; current is inversely proportional. More secondary turns gives higher voltage but lower current.

A transformer has $480\,\text{V}$ on $200$ primary turns and $50$ secondary turns. Find the secondary voltage.

$$V_s = V_p \times \frac{N_s}{N_p} = 480 \times \frac{50}{200} = 120\,\text{V}$$ This is a step-down transformer (ratio $4{:}1$).

For an ideal transformer, write the power-balance relationship between primary and secondary.

$$V_p \times I_p = V_s \times I_s$$ Since power in equals power out, stepping voltage down by a factor increases available current by the same factor.

Name the two main power-loss types in a transformer and how each is reduced.

Copper (I²R) losses in the windings, reduced by using larger/lower-resistance conductors. Core (iron) losses—hysteresis and eddy currents—reduced by using laminated, silicon-steel cores. Together they make real efficiency slightly below 100%.

What is the fundamental operating principle of an electric motor versus a generator?

A motor converts electrical energy into mechanical energy using the motor principle (force on a current-carrying conductor in a magnetic field, $F = BIL$). A generator converts mechanical energy into electrical energy using electromagnetic induction (Faraday's law). They are essentially the same machine run in reverse.

Define synchronous speed of an AC motor and give its formula.

Synchronous speed is the rotational speed of the stator's rotating magnetic field: $$N_s = \frac{120 \times f}{P}$$ where $f$ is frequency in hertz and $P$ is the number of poles; result in revolutions per minute (RPM).

Define percent slip in an induction motor and give its formula.

Slip is the difference between synchronous speed and actual rotor speed, which lets the rotor cut flux lines to produce torque: $$\%\,\text{slip} = \frac{N_s - N_r}{N_s} \times 100$$ where $N_s$ is synchronous speed and $N_r$ is rotor speed. An induction motor always runs slightly below synchronous speed.

What is counter-EMF (back-EMF) in a motor and why is starting current high?

As a motor's armature spins, it acts as a generator producing a voltage that opposes the supply—counter-EMF (CEMF). At startup the rotor is not turning, so CEMF is zero and current is very high (inrush/locked-rotor current); as speed rises, CEMF increases and running current drops to its normal value.