Electrical Theory for Journeyman Electrician Test: Foundational Laws
Ohm's Law and Its Practical Applications
Ohm’s Law serves as the fundamental building block for nearly every calculation on the licensing exam. It defines the linear relationship between voltage (E), current (I), and resistance (R), expressed through the primary formula E = I x R. For a journeyman candidate, the challenge is rarely the formula itself but its application in troubleshooting scenarios. For instance, if a heating element is rated for 240V but is connected to a 208V circuit, you must use Ohm’s Law to determine the resulting change in current and heat output.
On the exam, you will often be required to rearrange these variables to find a missing value. If a circuit has a known resistance of 12 ohms and is drawing 10 amperes, the voltage drop across that load is 120V. Understanding this relationship is critical for identifying voltage drop issues in long conductor runs. Excessive resistance in a wire—often caused by undersized conductors or poor terminations—results in a lower voltage available at the equipment, which can lead to premature motor failure or inefficient heater operation. Scoring well on these questions requires precision; even a small decimal error can lead to selecting the wrong multiple-choice option, as examiners often include "distractor" answers based on common calculation mistakes.
Kirchhoff's Voltage and Current Laws
Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) provide the framework for analyzing circuit behavior beyond a single load. KVL states that the algebraic sum of all voltages around a closed loop must equal zero. In practical exam terms, this means the sum of the voltage drops across all loads in a series circuit must equal the source voltage. If you are testing a series lighting string and measure different voltages at each lamp, KVL allows you to mathematically verify if the cumulative drop matches the 120V or 277V source.
KCL, conversely, focuses on the junctions or "nodes" within a circuit. It dictates that the total current entering a junction must exactly equal the total current leaving it. This is the underlying principle behind Parallel Circuits and is essential for understanding how neutral conductors carry unbalanced loads. On the journeyman test, KCL is often applied to multi-wire branch circuits. If a neutral wire in a 3-wire system carries 5 amps from Circuit A and 8 amps from Circuit B on the same phase (an NEC violation), KCL explains why the neutral current becomes additive, potentially overloading the conductor. Mastery of these laws ensures you can predict circuit behavior before applying a multimeter.
While Ohm's Law relates to the movement of electricity, power formulas describe the work being performed. The primary electrical formulas journeyman license candidates must memorize involve the Power Law (Watt’s Law): P = I x E. In the field and on the test, power is measured in Watts, representing the rate at which energy is consumed. Because many industrial loads are rated in Volt-Amps (VA) rather than Watts, understanding the distinction between apparent power and true power is vital for correct equipment sizing.
Advanced questions may require you to combine Ohm’s Law and the Power Law, resulting in formulas like P = I²R or P = E²/R. The P = I²R formula is particularly important for understanding heat loss in conductors. If you double the current flowing through a wire, the heat generated (power loss) increases by a factor of four, not two. This exponential relationship explains why the NEC is so stringent regarding overcurrent protection and conductor ampacity. Exam questions may ask you to calculate the total energy consumed over time, requiring you to convert Watts to Watt-hours or Kilowatt-hours (kWh). Precision in these power calculations journeyman tasks is essential for passing the theory portion of the exam.
Analyzing Series, Parallel, and Combination Circuits
Resistance, Voltage, and Current in Series Circuits
In a series circuit, there is only one path for electron flow. This simplicity leads to three rigid rules that are frequently tested. First, the total resistance (Rt) is the sum of all individual resistances (R1 + R2 + R3...). Second, the current (I) remains constant throughout the entire loop; the amperage measured at the source is identical to the amperage measured at the furthest load. Third, the total voltage is divided among the loads based on their proportional resistance.
Exam scenarios often use series circuits to test your understanding of Control Loops or old-style lighting strings. A common question might involve calculating the voltage drop across a specific resistor in a series of three. If the total voltage is 120V and the resistors are 10, 20, and 30 ohms, you must first find the total resistance (60 ohms), determine the circuit current (120V / 60Ω = 2A), and then apply Ohm’s Law to the specific component (2A x 20Ω = 40V). Recognizing that the largest resistor always consumes the most voltage in a series configuration is a key conceptual shortcut for verifying your math during the timed exam.
Rules Governing Parallel Circuit Behavior
Most modern electrical installations, from residential receptacles to industrial motor banks, are wired in parallel. In these systems, the voltage remains constant across all branches, while the total current is the sum of the currents in each individual branch. This is the opposite of series behavior and requires a different mathematical approach for calculating total resistance. The Reciprocal Formula (1/Rt = 1/R1 + 1/R2 + 1/R3...) is the standard method for determining the equivalent resistance of a parallel network.
For the journeyman test, a critical rule to remember is that the total resistance in a parallel circuit will always be less than the resistance of the smallest individual branch. If you calculate an answer that is higher than any single branch resistor, you have made an error in your reciprocals. This principle explains why adding more loads to a circuit increases the total current draw: as you add parallel paths, you decrease the overall resistance, allowing more electrons to flow from the source. Understanding this is fundamental to AC and DC circuit analysis exam sections, particularly when calculating the required size for a main service feeder that must support multiple parallel branch circuits.
Solving Complex Combination Circuit Problems
Combination circuits, also known as series-parallel circuits, require a systematic approach called Circuit Reduction. These problems are designed to test your ability to logically deconstruct a complex system into its simplest components. To solve these, you must identify segments of the circuit that are purely in parallel or purely in series, calculate their equivalent resistance, and redraw the circuit mentally or on scratch paper until only a single resistance value remains.
On a journeyman exam, a combination circuit might represent a real-world scenario where a motor (series component) is connected to a control panel with multiple indicator lights (parallel components). You might be asked to find the total current or the voltage available at a specific node. The key is to work from the point furthest from the power source back toward the source. Once the total resistance and total current are found, you then work "outward" again to find individual voltages and currents. This level of analysis demonstrates a candidate's ability to handle complex DC circuit analysis and is often a high-point-value area of the examination.
Alternating Current (AC) Fundamentals and Impedance
Sine Waves, Frequency, and Period
Unlike direct current (DC) which flows in one direction, alternating current reverses direction periodically, following a sinusoidal waveform. This transition introduces variables such as Frequency (measured in Hertz) and Period. In North America, the standard frequency is 60 Hz, meaning the current completes 60 full cycles (one positive and one negative alternation) per second. The period is the time required for one cycle, which at 60 Hz is approximately 0.0167 seconds.
Exam questions often focus on the relationship between peak voltage and Root Mean Square (RMS) voltage. Because an AC sine wave is constantly changing, its "effective" value for doing work is less than its peak. The RMS value is calculated as 0.707 times the peak voltage. When a voltmeter reads 120V, it is providing the RMS value, not the peak (which would be approximately 170V). Understanding this distinction is vital when selecting components like capacitors or insulation, which must be rated to handle the peak voltage stress rather than just the effective working voltage. You must be comfortable converting between Peak, Peak-to-Peak, and RMS values to satisfy various exam prompts.
Inductive and Capacitive Reactance
In AC circuits, resistance is not the only force that opposes current flow. Inductive Reactance (XL) and Capacitive Reactance (XC) play major roles whenever coils (motors, transformers) or capacitors are present. Inductive reactance is created by the self-induced back-electromotive force (BEMF) in a coil, which opposes changes in current. The formula XL = 2πfL shows that as frequency (f) or inductance (L) increases, the opposition to current increases. Crucially, in a purely inductive circuit, the current lags the voltage by 90 degrees.
Capacitive reactance is the opposition to the change of voltage across a capacitor. The formula XC = 1 / (2πfC) reveals an inverse relationship: as frequency or capacitance increases, the reactance decreases. In a purely capacitive circuit, the current leads the voltage by 90 degrees. These concepts are central to understanding power factor. Most industrial loads are inductive, causing the current to lag. To correct this and improve efficiency, capacitors are added to the system to provide leading current, effectively canceling out the lag. Journeyman candidates must be able to explain this phase shift and calculate reactance values using the standard frequency of 60 Hz.
Calculating Impedance in AC Circuits
Impedance (Z) is the total opposition to current flow in an AC circuit, combining resistance, inductive reactance, and capacitive reactance. Because these forces act at different phase angles, they cannot be added together mathematically (e.g., 10 ohms of R plus 10 ohms of XL does not equal 20 ohms of Z). Instead, they must be added vectorially using the Pythagorean theorem: Z = √ (R² + (XL - XC)²). This calculation represents the hypotenuse of the Impedance Triangle.
On the exam, you may be asked to calculate the total impedance of a motor winding that has both internal resistance and significant inductance. Once Z is determined, Ohm’s Law is modified for AC as E = I x Z. Understanding impedance is critical for calculating the fault current in a system. During a short circuit, the only thing limiting the current flow is the impedance of the path. If the impedance is too low, the fault current can exceed the Interrupting Rating of the circuit breaker, leading to catastrophic equipment failure. Mastering Z calculations is therefore a matter of both theoretical knowledge and practical safety.
Three-Phase Power Systems and Calculations
Delta and Wye Configurations
Three-phase power is the standard for industrial and commercial applications due to its efficiency and ability to provide constant torque for motors. The two primary ways to connect three-phase components are Wye (Y) and Delta (Δ). In a Wye configuration, one end of each of the three windings is connected to a common neutral point. This setup is common for distribution because it provides two different voltages (e.g., 120V and 208V or 277V and 480V).
In a Delta configuration, the three windings are connected end-to-end in a closed loop, forming a triangle. Delta systems are frequently used for power transmission and for heavy industrial motors that do not require a neutral. A key concept for the exam is the "High-Leg" Delta, where one phase-to-neutral voltage is significantly higher than the others (typically 208V in a 240V system). Identifying the High-Leg (usually identified by orange tape or insulation) is a frequent exam topic because connecting a 120V load to this leg will immediately destroy the equipment. Candidates must recognize these configurations on schematic diagrams and understand their grounding requirements.
Line vs. Phase Voltage and Current Relationships
Understanding the mathematical relationship between line values (measured between any two hot wires) and phase values (measured across a single winding) is essential for three-phase calculations. In a Wye System, the line current (IL) is equal to the phase current (Ip), but the line voltage (EL) is √3 (approximately 1.732) times the phase voltage (Ep). This is why 120V multiplied by 1.732 equals 208V.
Conversely, in a Delta System, the line voltage is equal to the phase voltage, but the line current is √3 times the phase current. This distinction is a common trap on the journeyman exam. For example, if you are told that each winding of a delta-connected motor draws 10 amps, the current flowing through the actual feeder wires (the line current) is 17.32 amps. Failing to apply the √3 factor will lead to undersizing conductors and overcurrent protection. You must always identify the connection type (Wye or Delta) before selecting which formula to apply to a three-phase problem.
Calculating the total power in a three-phase system requires the integration of the √3 constant and the Power Factor (PF). The formula P = √3 x E x I x PF is used to find the true power in Watts. If the question asks for apparent power in VA, the PF variable is omitted. The inclusion of √3 accounts for the fact that the three phases are 120 degrees out of sync, meaning the total power is not simply the sum of three single-phase loads but is slightly less due to the phase overlap.
On the exam, you might be given the horsepower (HP) of a motor and asked to find the required current. This requires a multi-step process: convert HP to Watts (1 HP = 746 Watts), then use the three-phase power formula to solve for I, factoring in the motor's efficiency and power factor. If a motor is 90% efficient, you must divide the output power by 0.90 to find the input power required from the source. These transformer theory and calculations often overlap with motor theory, requiring a holistic understanding of how power is transformed and consumed in an industrial facility.
Transformers operate on the principle of Mutual Induction, where a changing magnetic field in a primary coil induces a voltage in a secondary coil. The relationship between the primary and secondary is determined by the turns ratio. The fundamental formula is Vp / Vs = Np / Ns, where V is voltage and N is the number of turns in the winding. If the primary has 1000 turns and the secondary has 100 turns, it is a 10:1 step-down transformer.
Crucially, the relationship for current is inverse to voltage: Is / Ip = Np / Ns. As voltage is stepped down, the current is stepped up proportionally. This is why the secondary conductors of a step-down transformer are often much larger than the primary conductors. On the journeyman test, you will likely encounter questions asking you to calculate the secondary voltage or current given the primary values and the turns ratio. You must also understand the concept of a Tap on a transformer, which allows for minor adjustments to the turns ratio to compensate for voltage drop in the supply lines.
No transformer is 100% efficient; some energy is always lost as heat. These losses are categorized into two types: Core Losses (or iron losses) and Copper Losses. Core losses are caused by eddy currents and hysteresis within the magnetic steel core and remain constant regardless of the load. Copper losses, however, are caused by the resistance of the windings (I²R) and increase as the load on the transformer increases.
Exam questions may ask about the factors that affect transformer efficiency or the purpose of cooling methods like oil-immersion or forced-air fans. A transformer’s rating is always given in kVA (kilovolt-amps) rather than Watts because the manufacturer does not know the power factor of the load that will be connected. If you connect a highly inductive load with a poor power factor, the transformer may reach its thermal limit (kVA limit) before the actual work (Watts) reaches the desired level. Understanding this distinction is vital for ensuring that transformer theory and calculations are applied correctly in the field to prevent overheating.
Sizing a transformer involves more than just matching the total wattage of the loads. You must calculate the Total Connected Load in VA and then apply demand factors as permitted by the NEC. For example, if you are sizing a transformer for a continuous load, you must generally size the unit at 125% of that load to prevent excessive heat buildup.
On the exam, you might be presented with a scenario involving multiple motors and lighting loads. You would first calculate the VA for the lighting, then add the VA for the motors (using the Full-Load Amps from NEC tables, not the nameplate). The transformer must be able to handle the largest motor's starting current (Locked-Rotor Current) without causing an excessive voltage dip that would drop out other sensitive equipment. Mastering these electrical formulas journeyman license requirements allows you to select a transformer that is neither dangerously undersized nor unnecessarily expensive for the installation.
Motor Theory and Control Circuit Fundamentals
AC Motor Operation (Induction Motors)
Most industrial motors are squirrel-cage Induction Motors. They operate by creating a rotating magnetic field in the stator, which induces a current in the rotor. This induced current creates its own magnetic field, which interacts with the stator's field to produce torque. A key concept here is Slip, which is the difference between the synchronous speed (the speed of the magnetic field) and the actual speed of the rotor. Without slip, no current would be induced in the rotor, and no torque would be produced.
Questions on the journeyman test often address the factors that determine motor speed. The formula is Speed = (120 x Frequency) / Number of Poles. By changing either the frequency (using a Variable Frequency Drive) or the number of poles in the winding, the RPM of the motor can be controlled. Understanding this relationship is essential for troubleshooting why a motor might be running at the wrong speed or failing to start under load. You may also be tested on the difference between a squirrel-cage motor and a wound-rotor motor, focusing on how resistance is used to control starting torque.
Motor Full-Load Current and Locked-Rotor Current
There is a massive difference between the current a motor draws while running and the current it draws while starting. Full-Load Amps (FLA) is the current drawn at the rated horsepower and voltage. Locked-Rotor Amps (LRA) is the inrush current when the motor is first energized and the rotor is not yet turning. LRA can be 6 to 10 times higher than FLA.
For the exam, you must use the NEC tables (such as Table 430.250) to find the FLA for calculations involving branch-circuit conductors and overcurrent protection, rather than the motor nameplate. This ensures a standardized level of safety regardless of the specific motor manufacturer. You will also need to understand the function of Overload Protection. Unlike a circuit breaker, which protects against short circuits (high magnitude, short duration), an overload heater protects the motor from drawing slightly too much current over a long period, which would eventually destroy the winding insulation. Understanding these motor control circuit principles is a core requirement for any licensed journeyman.
Interpreting Basic Motor Control Ladder Diagrams
Motor control circuits use a specialized schematic called a Ladder Diagram or line diagram. In these drawings, the vertical rails represent the power source, and the horizontal rungs contain the control devices (buttons, switches, sensors) and the loads (coils, lights). A journeyman must be able to trace the flow of electricity through these rungs to determine the sequence of operation.
Common components include Normally Open (NO) and Normally Closed (NC) contacts. On the exam, you may be asked to identify a "holding circuit" or "seal-in circuit," where an auxiliary contact on a motor starter is wired in parallel with a momentary start button. This allows the motor to continue running after the operator releases the button. Understanding the logic of interlocking—where one motor cannot start until another is already running—is also a frequent topic. Being able to translate a physical wiring scenario into a ladder logic diagram, or vice versa, demonstrates the high-level troubleshooting skills expected of a licensed electrician.