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How do you know if your wiring will provide a reasonable efficiency of operation? The National Electrical Code, 210-19(a) (FPN 4) and 215-2 (b) (FPN 3), recommends 5% voltage drop for feeder circuits and 3% for branch circuits. Let's work some examples, using the equations in the sidebar (right). Our examples use uncoated copper wire in steel conduit, for 480V branch circuits; we'll use NEC Table 9's power factor column.
Example 1: Determine voltage drop
Run a No. 10 stranded wire 200 ft at 20A.
Per Table 9, our "ohms to neutral per 1,000 ft" is 1.1 ohms. To complete the numerator, multiply as follows: (2 x 0.866) x 200 ft x 1.1 ohms x 20A = 7,620.8 Dividing 7,621 by 1,000 ft gives a voltage drop of 7.7V. This drop is acceptable for our 480V circuit. A No. 12 would drop 11.8V. Boost the length to 500 ft, and that No. 10 drops 18V; the No. 12 drops 29V.
Example 2: Determine wire size
Run a stranded copper wire 200 ft at 20A.
You can find the wire size by algebraically altering the first equation, or you can use the following method. To complete the numerator, multiply as follows: 1.73 x 212.9 ohms x 200 ft x 20A = 89,371.2. Dividing the 89,371.2 by the acceptable voltage drop of 14.4V gives you 6,207 circular mils. NEC Table 8 shows that a No. 12 wire satisfies the voltage drop recommendation.
Example 3: Determine wire length
Run a stranded copper No. 10 wire for a 20A circuit.
To complete the numerator, multiply as follows: 1,000 x 14.4V = 14,400. To complete the denominator, multiply as follows: (2 x 0.866) x 1.1ohms x 20A = 38.104. Finally, divide the numerator by the denominator, as follows: 14,400 ÷ 38.104 = 378 ft. If you ran the No. 12 wire for the same circuit, you could run it 244 ft.
Example 4: Determine maximum load
Run a stranded copper No. 10 wire for a 200 ft circuit.
To complete the numerator, multiply as follows: 1,000 x 14.4V = 14,400. To complete the denominator, multiply as follows: (2 x 0.866) x 1.1 ohms x 200 ft = 381.04. Finally, divide the numerator by the denominator, as follows: 14,400 ÷ 381.04 = 37A. This circuit could handle 37A on each phase conductor. A 200 ft No. 2 could handle 24A.
* The number "0.866" is for 3-phase only. It converts the number "2" to "1.732" (the square root of 3). For single-phase circuits, don't use the "0.866" in the calculations.
* "CM"denotes wire size in circular mils, as shown in Table 8.
* To calculate wire size, use 12.9 as your K for copper and 21.2 as your K for aluminum.
* "L" is the one-way wire length in ft.
* "R" is the resistance per 1,000 ft. Use NEC Table 9 for AC wiring. If you have non-linear loads, use the column that helps account for power factor.
Equation 1: Calculating the actual Voltage Drop I[Volts dropped = (2 x 0.866) x L x R x Amps/1,000]
Equation 2: Calculating the Wire Size in circular mils [CM = 2 x K x L x Amps/Acceptable Voltage Drop]. Alternatively, you can algebraically manipulate Equation 1 to: Acceptable Voltage Drop ÷ 1.732 x L x Amps and then look up the wire size according to its AC resistance.
Equation 3: Calculating the Length in ft [Length = 1,000 x Acceptable Voltage Drop ÷ (2 x 0.866) x R x Amps]
Equation 4: Calculating the Load in amps [Amps = 1,000 x Acceptable Voltage Drop ÷ (2 x 0.866) x R x L]
