CSLB C-10 Electrical ContractorEquipment and InstallationHard
A 120-volt lighting branch circuit uses 12 AWG copper conductors (K=12.9) to supply a 12-ampere load located 150 feet from the panel (one-way distance). Using the formula VD = (2 × K × I × D) / CM, what is the approximate percentage voltage drop on this circuit?
- A7.1%
- B2.9%
- C5.9%
- D4.5%
Show answer & explanationAnswer & explanation
Correct answer: C. 5.9%
12 AWG has a circular mil area of 6,530 CM. VD = (2 × 12.9 × 12 × 150) / 6,530 = 46,440 / 6,530 ≈ 7.11 volts. As a percentage of 120V, this is 7.11/120 ≈ 5.9%, which exceeds the 3% recommended limit for branch circuits, indicating a larger conductor should be used.
Why the other options are wrong
- A. 7.1% incorrectly treats the calculated voltage (7.11V) as the percentage rather than converting it relative to 120V.
- B. 2.9% is well below the actual calculated drop and would only apply to a much shorter run or larger conductor.
- D. 4.5% underestimates the drop; the correct calculation yields a higher percentage.
Voltage Drop Calculation
Voltage drop is calculated using VD = (2 × K × I × D) / CM for single-phase circuits, where K is the resistivity constant, I is current, D is one-way distance, and CM is circular mils.
- Copper K ≈ 12.9; Aluminum K ≈ 21.2
- NEC recommends max 3% for branch circuits, 5% total (feeder+branch)
- Formula uses one-way distance but factor of 2 accounts for round trip
Memory trick: Double the distance current travels, divide by wire's circular mils.