Circuit Calculations (Ohm's Law)

Circuit Calculations (Ohm's Law)

Learning Objectives

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

1.1 Fundamental Units and Definitions

Before any calculation, you must be fluent in the base units:

Key relationships to memorize:

For AC circuits with reactance (motors, transformers), you must distinguish between:

For the Massachusetts Journeyman Part II exam, most circuit calculations assume resistive loads unless a motor or transformer is explicitly identified. When motors appear, use Article 430 and remember that the power factor is already accounted for in the nameplate full-load current (FLC) tables.

1.2 Series Circuits

In a series circuit, components are connected end-to-end so that the same current flows through each element.

Rules:

Practical method:

Field point: On a job site, a series circuit is rare in power distribution but common in control circuits (e.g., limit switches, safety interlocks). If a control circuit fails, measure voltage across each component to find the open device — the full source voltage will appear across the open element.

1.3 Parallel Circuits

In a parallel circuit, components are connected across the same two points, so each branch sees the full source voltage.

Rules:

Practical method:

Exam trap: Many candidates incorrectly apply the two-resistor product-over-sum rule to three or more resistors. That rule works only for exactly two parallel resistors. For three or more, use the reciprocal method.

Field point: In a lighting circuit with multiple receptacles or luminaires, the loads are in parallel. When you add a branch, total current increases, and you must verify the conductor ampacity and overcurrent device rating per NEC 210.19 and 210.20.

1.4 Series-Parallel (Combination) Circuits

These circuits contain both series and parallel sections. The solution strategy is always the same:

Example approach:

Exam trap: When you split the parallel voltage back into branch currents, do not use the total current for both branches. The sum of branch currents must equal the total current — use this as a check.

1.5 Voltage Drop — NEC 210.19(A)(1)

Voltage drop is a performance requirement, not a safety requirement. The NEC does not mandate a specific maximum voltage drop for branch circuits and feeders in most cases; however, 210.19(A)(1) Informational Note No. 4 recommends that conductors be sized so the voltage drop does not exceed 3% for a branch circuit or feeder, and 5% total from the service point to the farthest outlet.

Massachusetts note: 527 CMR 12.00 adopts the NEC with state amendments. For voltage drop, Massachusetts does not add a mandatory percentage beyond the NEC informational note, but the exam will expect you to know the 3%/5% figures and apply them when asked.

Voltage drop formula (single-phase):

VD = 2 × K × I × L / CM

Where:

Alternative formula (using ohms per 1000 ft):

VD = 2 × L × I × R / 1000

Where R is the conductor resistance in ohms per 1000 ft from NEC Chapter 9, Table 8.

Three-phase formula:

VD = 1.732 × K × I × L / CM

The factor 1.732 (√3) replaces the 2 because the current returns through a different phase conductor, reducing the effective loop length.

Percent voltage drop:

%VD = (VD / V_source) × 100

Practical method for sizing:

Exam trap: Always use the one-way length in feet, not the round-trip. The formula already includes the factor of 2 for the return path. Doubling the length again is a common error.

Field point: On site, voltage drop matters for long runs to subpanels, parking lot lighting, and equipment pads. A journeyman should measure actual conductor lengths — do not trust the tape measure from the panel to the device; include vertical rises, horizontal runs, and slack at both ends.

1.6 Conductor Ampacity vs. Load Calculation

Do not confuse ampacity (the current-carrying capacity of a conductor under specific conditions) with load calculation (the sum of expected loads). The NEC separates these concepts:

Minimum branch circuit conductor size is based on the load per 210.19(A)(1): the conductor must have an ampacity not less than the maximum load to be served. For continuous loads (3 hours or more), the load is calculated at 125% per 210.19(A)(1) and 210.20(A).

Exam trap: When a question says "continuous load," do not simply multiply the load by 1.25 for the conductor and then also multiply for the overcurrent device — you do both, but they are separate steps. The conductor ampacity must be ≥ 125% of continuous load; the overcurrent device rating must also be ≥ 125% of continuous load. If the conductor is already sized for the 125% factor, the breaker can match the conductor ampacity.

1.7 Motor Circuit Calculations (Article 430)

Motor calculations are a distinct subset because motors draw starting current well above running current, and the NEC provides specific rules.

Key sections:

Voltage drop for motors: When calculating voltage drop for a motor circuit, use the actual load current (which may be less than FLC) or the FLC from tables, depending on what the question asks. Do not use locked-rotor current (starting current) for voltage drop — that is a momentary condition.

Field point: A journeyman must read the motor nameplate for voltage, FLC, service factor, and temperature rise. The nameplate FLC is for overload sizing; the table FLC is for conductor and breaker sizing. Mixing these up is a classic exam failure.

1.8 Transformer Calculations

Transformers are covered under Article 450, but circuit calculations involving transformers require understanding the relationship between primary and secondary.

Basic relationships:

Sizing conductors for transformer secondaries:

Exam trap: For a single-phase transformer, the secondary full-load current is:

I_secondary = VA / V_secondary

For a three-phase transformer:

I_secondary = VA / (1.732 × V_secondary)

Field point: When connecting a step-down transformer, the primary current is lower than the secondary current. Many installers undersize the primary conductors because they look at the secondary load — always calculate both sides.

1.9 Power Factor and AC Circuits

For non-resistive loads (motors, fluorescent lighting ballasts, LED drivers), the power formula becomes:

P = V × I × pf

Where pf is the power factor (0 to 1).

Reactive loads:

Exam relevance: The Massachusetts exam rarely asks for power factor correction calculations, but you must understand that a motor's nameplate FLC already includes the effect of power factor. When using the NEC tables (430.247–430.250), the listed FLC values are based on typical motor power factors and efficiencies — you do not multiply by pf again.

1.10 Code Navigation — Where to Find It

Use this table to locate the governing rule during the open-book exam:

1.11 Common Exam Traps — Summary

1.12 Practical Field Points

1.13 Summary

Circuit calculations on the Massachusetts Journeyman Part II exam are not about memorizing formulas — they are about applying the correct formula to the correct situation and navigating the NEC to verify sizing requirements. Master the distinction between ampacity, load, voltage drop, and overcurrent protection. Know where each rule lives in the 2026 NEC. And always check your units and your arithmetic before marking the answer.

The open-book format rewards candidates who know where to look as much as those who know how to calculate. Use the Code Navigation table above as your map, and practice each calculation type until the steps are automatic.