Voltage drop calculations
Voltage drop on the exam is one formula. For a single-phase circuit, VD = 2 × K × I × L ÷ CM. For a three-phase circuit, the 2 becomes 1.732. K is the resistance constant of the metal, I is the load in amperes, L is the one-way length in feet, and CM is the circular-mil area of the conductor.
The method
- Read the phase. Single-phase uses the factor 2; three-phase uses 1.732.
- Pick K for the metal: 12.9 for copper and 21.2 for aluminum are the values exam problems are written with.
- Use the one-way distance. The factor already covers the return path.
- Look up the circular mils of the conductor size in Chapter 9, Table 8.
- Divide the result by the circuit voltage if the question asks for a percentage.
The 3 percent and 5 percent figures people quote come from informational notes in the Code. On the exam they are a limit only when the question says so.
Worked problems
Problem 1. A single-phase 120-volt circuit supplies a 70 A load through 3 AWG aluminum conductors. The one-way run is 75 feet. What is the approximate voltage drop?
Answer: 4.23 V
VD = 2 x K x I x L / CM. K = 21.2 for aluminum. 3 AWG has 52,620 circular mils (Chapter 9, Table 8). VD = 2 x 21.2 x 70 x 75 / 52,620 = 4.23 V, or 3.5% of 120 V. Use the ONE-WAY distance: the 2 factor already covers the return path.
Reference: NEC Chapter 9, Table 8 (circular mils); see 210.19(A) and 215.2(A) Informational Notes
Problem 2. A three-phase 208-volt circuit supplies a 100 A load through 3 AWG copper conductors. The one-way run is 325 feet. What is the approximate voltage drop?
Answer: 13.80 V
VD = 1.732 x K x I x L / CM. K = 12.9 for copper. 3 AWG has 52,620 circular mils (Chapter 9, Table 8). VD = 1.732 x 12.9 x 100 x 325 / 52,620 = 13.80 V, or 6.6% of 208 V. Use the ONE-WAY distance: the 1.732 factor already covers the return path.
Reference: NEC Chapter 9, Table 8 (circular mils); see 210.19(A) and 215.2(A) Informational Notes
Problem 3. A single-phase 240-volt circuit supplies a 45 A load through 8 AWG copper conductors. The one-way run is 150 feet. What is the approximate voltage drop?
Answer: 10.55 V
VD = 2 x K x I x L / CM. K = 12.9 for copper. 8 AWG has 16,510 circular mils (Chapter 9, Table 8). VD = 2 x 12.9 x 45 x 150 / 16,510 = 10.55 V, or 4.4% of 240 V. Use the ONE-WAY distance: the 2 factor already covers the return path.
Reference: NEC Chapter 9, Table 8 (circular mils); see 210.19(A) and 215.2(A) Informational Notes
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Common questions
What is the voltage drop formula for three-phase?
VD = 1.732 × K × I × L ÷ CM, with L as the one-way length in feet and CM from Chapter 9, Table 8.
Do I double the distance in a voltage drop problem?
No. Use the one-way length. The factor 2 in the single-phase formula already accounts for the return conductor.