Crash course: Ohm's Law for electricians contractor's perspective (part 4)

Why Part 4 Goes Deeper

Parts 1 through 3 covered the equation, the wheel, and basic single-phase loads. Part 4 is where Ohm's Law stops being a classroom exercise and starts paying for your truck. We're talking voltage drop on long runs, conductor sizing under 215.2(A)(1), and the math that keeps you out of trouble on a rough-in inspection.

Every value you calculate in the field traces back to E = I x R. Memorize it cold. The contractors who eat lunch on time are the ones who can run these numbers in their head while the GC is still asking questions.

Voltage Drop: The Calculation That Saves Callbacks

NEC 210.19(A) Informational Note No. 4 recommends branch circuits not exceed 3% voltage drop, with 5% total combined with the feeder. It's not enforceable as written, but inspectors in jurisdictions that adopted it as a local amendment will fail you. More importantly, motors, LED drivers, and POE switches downstream don't care what the code says. They care about volts at the terminal.

The single-phase formula you actually use on the job:

• VD = (2 x K x I x D) / CM
• K = 12.9 for copper, 21.2 for aluminum (at 75°C)
• D = one-way distance in feet
• CM = circular mils of the conductor (Chapter 9, Table 8)

Three-phase, drop the 2 and multiply by 1.732. Run a 200 ft branch at 20 amps on #12 copper and you're already at roughly 6.4 volts on a 120V circuit, over 5%. Bump to #10 and you cut it nearly in half.

Resistance Isn't Static

Conductor resistance climbs with temperature. Chapter 9, Table 8 lists DC resistance at 75°C, but a conductor pulling near its 310.16 ampacity in a hot attic is hotter than that. For long pulls in conduit fills approaching the 310.15(C)(1) adjustment thresholds, derate first, then check voltage drop on the derated conductor.

Splices, lugs, and loose terminations add resistance you can't see on the print. A 0.05 ohm bad connection on a 30 amp circuit dissipates 45 watts at the lug. That's the hot spot the IR camera finds three years later.

Field tip: if a breaker keeps tripping and the load math checks out, torque every termination on the circuit to the manufacturer's spec before you start swapping breakers. 110.14(D) requires it anyway, and a loose neutral mimics a dozen other faults.

Power Math When the Load Isn't Resistive

P = I x E works clean on heaters and incandescent. The minute you put a motor, VFD, or LED driver on the circuit, power factor enters the picture. True power in watts equals volts times amps times power factor. A 1 HP motor nameplate at 0.85 PF drawing 13 amps at 120V is pulling 1326 VA but only 1127 watts of real work.

For sizing conductors and overcurrent, you size to the VA, not the watts. NEC 430.6(A)(1) tells you to use Table 430.248 for single-phase motor FLA, not the nameplate, for conductor and OCPD sizing. Nameplate is for overload protection only under 430.32.

• Conductors and breakers: Table 430.247 through 430.250
• Overload relays: motor nameplate FLA
• Locked rotor and short circuit: Table 430.251(B)

Putting It Together on a Real Job

Say you're feeding a 7.5 HP, 240V single-phase compressor 175 ft from the panel. Table 430.248 gives 40 amps FLA. Conductor minimum is 125% per 430.22, so 50 amps. A #8 THHN copper handles that at 75°C per 310.16.

Now run voltage drop. VD = (2 x 12.9 x 40 x 175) / 16510 CM for #8 = 10.9 volts, about 4.5% on 240V. Acceptable for a motor branch but tight. Upsize to #6 and you drop to about 2.9%. The cost of the larger wire is less than one service call when the compressor starts nuisance tripping in July.

Field tip: always price voltage drop upgrades into the bid up front. Going back to the customer after the rough to explain why #8 won't work is a margin killer and a trust killer.

The Numbers Worth Memorizing

You don't need to carry a calculator for the common stuff. These are the values that come up on almost every residential and light commercial job. Burn them in.

1. 120V x 20A = 2400 VA, 80% continuous = 1920 VA usable per 210.19(A)(1)
2. 240V x 30A dryer circuit = 7200 VA, but use 5000 or nameplate per 220.54
3. #14 = 15A, #12 = 20A, #10 = 30A at 60°C column, 240.4(D) small conductor rule
4. K factor copper: 12.9. Aluminum: 21.2. Memorize both.
5. 1.732 is the square root of 3. Every three-phase calc uses it.

Ohm's Law isn't trivia. It's the foundation under every load calc, every conductor pick, every breaker you set. Part 5 will get into three-phase wye and delta math, where neutral current and unbalanced loads start writing their own rules.