The basics of calculating voltage drop

Mar 1, 1999 12:00 PM, Mark Lamendola

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 = 7620.8 Dividing 7621 by 1000 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 = 89371.2 Dividing the 89371.2 by the acceptable voltage drop of 14.4V gives you 6207 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: 1000 x 14.4V = 14400 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: 14400 / 38.1044377 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: 1000 x 14.4V = 14400 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: 14400 / 381.04437A 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 in volts Volts Dropped = (2 x 0.866) x L x R x Amps/1000

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: R410002Acceptable 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 = 1000 x Acceptable Voltage Drop/ (2 x 0.866) x R x Amps

Equation 4: Calculating the Load in amps Amps = 1000 x Acceptable Voltage Drop/ (2 x 0.866) x R x L

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