学习材料

Introduction

This is the smallest area by weight but the most practical — it connects the math of Ohm's law and power to the meters, testers, and methods an electrician uses to verify and diagnose circuits safely. Expect questions on choosing the right instrument, its category (CAT) rating, the live-dead-live verification habit, and identifying open, short, and ground faults.

Learning objectives

• Match the instrument to the measurement (DMM, clamp meter, megohmmeter, receptacle tester) and read CAT I–IV ratings.
• Apply Ohm's law (E = I × R) and the power formula (P = I × E), including P = I²R and P = E²/R.
• Connect a voltmeter in parallel and an ammeter in series, and perform a live-dead-live check.
• Identify open, short, ground-fault, reversed-polarity, and open-neutral conditions.
• State the torque and dissimilar-metals termination rules.

Part A — Test instruments and CAT ratings

• Digital multimeter (DMM): measures voltage, resistance, and (small) current; must be set to the correct function and range before connecting.
• Clamp meter: reads current by sensing the magnetic field around a single conductor, without opening the circuit — the tool of choice for measuring load amps on an energized feeder.
• Megohmmeter (megger): applies a high DC test voltage to measure insulation resistance in megohms, revealing degraded insulation before it fails. Used on de-energized conductors and windings.
• CAT (measurement category) rating: CAT I → CAT IV indicates the transient overvoltage a meter can survive; higher categories are closer to the service (CAT IV at the service entrance, CAT III at distribution, CAT II at receptacle-fed equipment). Use a meter rated at or above the location's category.
• Receptacle tester: a plug-in tester flags common miswires but cannot reliably detect a bootleg ground or every fault — it is a screening tool, not proof.

Part B — Ohm's law, power, and safe measurement

• Ohm's law: E = I × R — voltage equals current times resistance; any one value follows from the other two.
• Power formula: P = I × E, and equivalently P = I²R = E²/R. For a purely resistive load, watts = volt-amperes (power factor = 1).
• Voltmeter in parallel, ammeter in series: a voltmeter connects across a component; an ammeter connects in the path so current flows through it. Connecting an ammeter across a live source is a dead short.
• Verify the meter (live-dead-live): confirm the voltage tester works on a known live source before and after testing the circuit — the tester itself can fail.
• Start at the highest range when the value is unknown, then step down, to protect the meter and yourself.

Worked example — Ohm's law and power. A 120 V circuit feeds a purely resistive 1,500 W heater. Current: I = P / E = 1,500 / 120 = 12.5 A. Resistance: R = E / I = 120 / 12.5 = 9.6 Ω (check: R = E² / P = 14,400 / 1,500 = 9.6 Ω). Because it is resistive, 1,500 W = 1,500 VA. Source: standard electrical theory (Ohm's law and the power wheel).

Worked example — series resistance. Three 4 Ω resistors in series across 24 V: total R = 4 + 4 + 4 = 12 Ω; I = 24 / 12 = 2 A; power dissipated = I²R = 2² × 12 = 48 W (or P = E²/R = 576/12 = 48 W). In series the current is the same everywhere; in parallel the voltage is. Source: standard electrical theory.

Part C — Diagnosing faults

Most service calls reduce to a few fault types:

• Open circuit: a break in the path — no current, infinite resistance on a continuity test, and full source voltage across the break.
• Short circuit: an unintended low-resistance path that lets current bypass the load, causing high current that trips protection.
• Ground fault: unintended current to a grounded surface — what a GFCI is built to catch.
• Reversed polarity: hot and neutral swapped, energizing surfaces meant to be grounded — a shock hazard even though a device may still "work."
• Open neutral (multiwire circuit): shifts voltage between the two legs, making lights brighten and dim and damaging equipment.
• Continuity only when de-energized: an ohmmeter applies its own source; using it on a live circuit damages the meter and gives false readings.

Exam trap — voltage across an open, not across a short. On an open, your voltmeter reads full voltage across the break (no current, no drop elsewhere). On a short, current soars and the breaker trips. Candidates reverse these. Remember: open = full voltage present, no current; short = huge current, protection opens.

Part D — Grounding checks, phase rotation, and terminations

• Verify equipment grounding: confirm a low-resistance path from equipment enclosures back to the source, so a fault trips the breaker instead of energizing the metal.
• Phase rotation: a phase-rotation meter confirms the sequence of a three-phase supply so motors turn the intended direction before final connection (swap any two leads to reverse).
• Torque terminations (110.14): terminals must be tightened to the manufacturer's specified torque — both loose and over-tight connections fail and overheat. Use a calibrated torque tool, not feel.
• Dissimilar metals (110.14): use terminals identified for the conductor material; copper-to-aluminum requires listed connectors and antioxidant per listing.
• Commissioning check: before energizing, verify labeling, torque, insulation resistance, and grounding so the system starts up safely.

Part E — Three-phase, power factor, and the numbers behind the meter

C-10 work is not just single-phase houses; commercial services are three-phase, and a few theory questions test whether you understand it.

• Line vs. phase. In a wye (Y) system the line-to-line voltage is √3 (1.732) times the line-to-neutral voltage — that is why 208Y/120 and 480Y/277 exist (120 × 1.732 ≈ 208; 277 × 1.732 ≈ 480). In a delta system the line current is √3 times the phase current.
• Three-phase power: P = 1.732 × Eline × Iline × PF. For a balanced resistive load PF = 1 and the 1.732 factor is the whole story.
• Power factor is the ratio of real power (watts) to apparent power (VA). Motors and other inductive loads pull PF below 1, so the current for a given wattage rises — which is why utilities bill demand in kVA and why capacitor correction exists. On the exam, watch for "watts vs. VA": for a resistive load they are equal; for an inductive load they are not.
• Balanced vs. unbalanced. A balanced three-phase load puts little or no current on the neutral; an unbalanced one (mixed single-phase loads) loads the neutral with the difference — the same unbalance idea as the dwelling neutral.

Worked example — three-phase current. A balanced 30 kW resistive load on a 480 V, three-phase feeder draws: I = P ÷ (1.732 × E) = 30,000 ÷ (1.732 × 480) = 30,000 ÷ 831 = 36.1 A per line. (Single-phase at 240 V, the same 30 kW would be 125 A — three-phase moves more power on smaller conductors, a core reason commercial services are three-phase.) Source: three-phase power formula.

Key numbers & facts — Testing & Troubleshooting - E = I × R; P = I × E = I²R = E²/R - Voltmeter parallel; ammeter series; start on the highest range - Live-dead-live: verify tester before and after - Clamp meter = current without opening the circuit; megohmmeter = insulation resistance (de-energized) - CAT rating: higher = closer to the service; use ≥ the location's category - Open = infinite Ω / full voltage across the break; short = high current, trips; ground fault = current to ground - Continuity tests only de-energized - Torque to manufacturer spec — §110.14

Chapter self-check

1. A 240 V element draws 20 A — its resistance and power? (R = 12 Ω; P = 4,800 W.)
2. Which instrument reads insulation resistance? (Megohmmeter, de-energized.)
3. Where do you connect an ammeter? (In series.)
4. Full voltage across a break with no current indicates what fault? (An open circuit.)

Chapter summary

Small area, high practicality. Own Ohm's law and the power wheel, connect meters correctly (voltmeter parallel, ammeter series), and never trust a "dead" reading without a live-dead-live check. Diagnose by symptom: open = full voltage/no current, short = trips, ground fault = current to ground, and always run continuity de-energized.

Sources: standard electrical theory (Ohm's law, power formula, series/parallel, three-phase rotation); instrument practice (DMM, clamp meter, megohmmeter, CAT ratings, receptacle testers); NEC (NFPA 70) §110.14 (torque and dissimilar-metal terminations). Theory calculations independently recomputed.