Chapter 3: Circuits, AC Concepts, and Voltage Drop

Chapter 2 gave you Ohm's law and power. This chapter puts those tools to work on the kinds of circuits electricians actually build — and on voltage drop, a dedicated scoring area on Utah's Journeyman exam.

3.1 Series Circuits in the Field

True pure-series power wiring is uncommon for outlets (we parallel loads so each sees full voltage), but series thinking shows up everywhere:

• Voltage drops along a long feeder
• Multi-wire connections where improper neutrals create series surprises
• Troubleshoot: an open in a series string kills everything downstream

Rules to keep sharp:

• Current is the same at every point in a series loop.
• Voltages add to the source.
• An open anywhere stops all current.

3.2 Parallel Circuits in the Field

Branch-circuit loads are almost always in parallel across the same voltage.

Rules:

• Voltage is (ideally) the same across each branch.
• Currents add to the total.
• Opening one branch does not stop the others.
• Adding more loads decreases total resistance and increases total current.

Example. On a 120 V circuit, three loads draw 2 A, 3 A, and 5 A.

[ I_T = 10 A,R_{eq} = = 12  ]

3.3 Multiwire Branch Circuits

A common residential/commercial arrangement uses two ungrounded ("hot") conductors with opposite legs / phases and a shared neutral (grounded conductor).

On a 120/240 V single-phase system:

• Each hot to neutral is 120 V.
• Hot to hot is 240 V.
• Neutral carries the difference of the two hot currents when the hots are on opposite legs.

If both hots are on the same leg (miswired), the neutral can carry the sum — a serious overload risk. Handle-tied or common-trip breakers, correct phasing, and identifying neutrals matter.

Exam theme: neutrals are current-carrying conductors in normal operation. Do not confuse them with equipment grounding conductors.

3.4 Introduction to AC Waveforms

AC voltage and current vary with time, typically as a sine wave at 60 Hz in the U.S.

Important values:

• Peak — maximum instantaneous value
• Peak-to-peak — from positive peak to negative peak
• RMS (root mean square) — the effective value that produces the same heating in a resistor as a DC value of that magnitude

For a sine wave:

[ E_{RMS} = 0.707 E_{peak} ]

[ E_{peak} = 1.414 E_{RMS} ]

When someone says "120 volts," they almost always mean 120 V RMS. Meters used for power work display RMS for sine waves (true-RMS meters needed for distorted waveforms).

3.5 Frequency, Period, and Wavelength (Light Touch)

[ f = ]

At 60 Hz, the period (T) is 1/60 second. You rarely calculate this on the electrician exam, but transformers, motors, and capacitive/inductive behavior all assume the system frequency.

3.6 Resistance, Inductance, and Capacitance

Real AC circuits contain more than resistance.

Property	Symbol	Opposes / stores	Phase note
Resistance	(R)	Dissipates energy as heat	V and I in phase
Inductance	(L) (henry)	Opposes change in current	Current lags voltage
Capacitance	(C) (farad)	Opposes change in voltage	Current leads voltage

Inductive reactance:

[ X_L = 2f L ]

Capacitive reactance:

[ X_C = ]

Impedance (Z) is the AC equivalent of resistance for Ohm's law:

[ E = I Z ]

For a series R–L–C type relationship (magnitudes):

[ Z = ]

3.6.1 Power factor

[ PF = = = ]

• Purely resistive: PF = 1
• Motors (inductive): PF lagging, often 0.7–0.9 unloaded vs loaded varies
• Utility and large facilities care about PF; exam questions may ask you to find true power from VA and PF

Example. A load draws 10 A at 240 V. Metered true power is 1920 W.

[ VA = 240 = 2400,PF = 1920/2400 = 0.8 ]

3.7 Transformers (Theory You Need)

Transformers change AC voltage using magnetic coupling. Ideal approximate relationships:

[ = = ]

Power in ≈ power out (ignoring losses):

[ E_P I_P E_S I_S ]

Example. 480 V primary, 120 V secondary, secondary load 10 A. Approximate primary current:

[ I_P = 2.5 A ]

Utah's practical exam includes transformer termination for unlimited electrician candidates — matching conductors to correct points on a Delta-Wye transformer. Theory here supports that hands-on task: know high/low voltage sides, neutral/X0 where applicable, and that wrong landing points create dangerous voltages.

3.7.1 Separately derived systems

A transformer with no direct electrical connection between primary and secondary is a classic separately derived system. It needs its own grounding/bonding treatment under Article 250 — foreshadowing Chapter 6.

3.8 Voltage Drop: Why It Matters

Voltage drop is the reduction in voltage from source to load caused by conductor resistance (and, more completely, impedance). Excessive drop causes:

• Dim lights
• Motors that overheat or fail to start
• Nuisance issues on electronics
• Customers who blame "bad power" when the feeder is simply undersized or too long

The NEC informational notes recommend (not always a mandatory "shall") limiting drop to roughly:

• 3% on branch circuits or feeders individually in many notes
• 5% total (feeder + branch) as a common design target

Exam questions may ask you to calculate drop, or to size wire so drop stays under a stated percentage. Read carefully whether the question uses one-way length or round-trip.

3.9 Voltage Drop Formulas

3.9.1 Single-phase (most common exam form)

[ VD = ]

Where:

• (VD) = voltage drop (volts)
• (K) = direct-current resistance constant (copper ≈ 12.9, aluminum ≈ 21.2 in many Ugly's/exam sheets — use the value the problem or your allowed reference specifies)
• (I) = current in amperes
• (D) = one-way distance in feet
• (CM) = circular mil area of the conductor
• The 2 accounts for the outgoing and return conductors

3.9.2 Three-phase

[ VD = ]

(Uses () instead of 2 for balanced three-phase line conductors.)

3.9.3 Percent voltage drop

[ %VD = ]

3.9.4 Finding required CM for a maximum drop

Rearrange single-phase:

[ CM = ]

Then choose the next larger standard conductor size from NEC Chapter 9 Table 8 (or Ugly's).

3.10 Worked Voltage Drop Problems

Problem A. A 120 V single-phase branch circuit supplies 16 A. One-way length is 90 ft. Conductor is 12 AWG copper (6530 cmil). Use (K = 12.9).

[ VD =  V ]

[ %VD = % ]

That exceeds a 3% branch-circuit design target — you might upsize the wire.

Problem B. Same load and length, but 10 AWG copper (10380 cmil):

[ VD =  V % ]

Problem C. 208 V three-phase feeder, 40 A, 200 ft one-way, 1 AWG copper (83690 cmil), (K = 12.9):

[ VD =  V ]

[ %VD = % ]

Problem D. What minimum CM is needed for 240 V single-phase, 30 A, 150 ft, max 3% drop, copper (K=12.9)?

[ VD_{max} = 0.03 = 7.2 V ]

[ CM = = 16125  ]

6 AWG copper is 26240 cmil; 8 AWG is 16510 cmil — 8 AWG is just enough by this math (always confirm ampacity and termination temperature ratings too; voltage drop never overrides ampacity rules).

3.11 Using Tables Instead of (K)

Ugly's and many exam prep sheets also provide voltage drop tables or ohms-per-1000-feet methods:

[ VD = I R ]

for single-phase, where (R) is ohms per 1000 ft from the conductor table at the appropriate temperature. Same idea, different packaging. Use whichever form matches the given data.

3.12 Skin Effect and AC Resistance (Awareness)

At larger sizes and AC, effective resistance rises slightly versus DC (skin effect). Precision design may use AC impedance tables. For typical branch-circuit exam problems, the standard (K) method is what you will use.

3.13 Troubleshooting With Voltage Drop Thinking

If voltage at a panel is fine but voltage at a load is low:

1. Measure under load (drop appears when current flows).
2. Check conductor size and length.
3. Check for loose neutrals/hots (connection resistance adds drop and heat).
4. Check shared neutrals and overloaded multiwire circuits.
5. Check for undersized extension cords or temporary wiring.

3.14 Practice Problems

1. Series: 10 Ω and 30 Ω on 120 V. Find current and voltage across the 30 Ω resistor.
2. Parallel: loads of 4 A and 12 A on 120 V. Find total current and equivalent resistance.
3. A load is 1800 VA at 120 V, PF 0.75. Find current and true power.
4. Single-phase VD: 20 A, 120 ft one-way, 10 AWG Cu (10380 cmil), (K=12.9), 120 V system. Find volts dropped and %VD.
5. What CM is required for 3% max drop: 240 V, 50 A, 180 ft, single-phase copper, (K=12.9)?
6. Transformer: 480 V to 240 V, secondary delivers 25 A. Approximate primary current (ignore losses).

3.14.1 Answers

1. (R_T=40) Ω, (I=3) A, (V_{30}=90) V.
2. (I_T=16) A, (R_{eq}=7.5) Ω.
3. (I = 1800/120 = 15) A; (P = 1800 = 1350) W.
4. (VD = (2)/10380 ) V; (%VD %).
5. (VD_{max}=7.2) V; (CM=(2)/7.2 = 32250) cmil → next standard size at least 4 AWG (41740 cmil) after checking ampacity.
6. (I_P (240)/480 = 12.5) A.

3.15 Looking Ahead

You can now quantify how wire size and length steal voltage from a load. Chapter 4 turns to the hardware itself: conductor types, ampacity, cables, raceways, and enclosures — the Code side of getting current from the panel to the load without cooking the insulation.

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