Crash course: Ohm's Law for electricians master-level deep dive (part 2)

Picking Up Where Part 1 Left Off

Part 1 covered V=IR, power math, and branch circuit sizing. Part 2 goes where the rubber meets the conduit: voltage drop across long runs, impedance in AC systems, fault current math, and how Ohm's Law interacts with NEC 210.19(A), 215.2, and 310.15 conductor ampacity tables.

If you can't derive the voltage at the far end of a 400 foot feeder in your head within 10%, this post is for you. Journeyman electricians should be comfortable with everything here. Masters should be able to teach it.

Voltage Drop on Real Runs

NEC 210.19(A) Informational Note No. 4 recommends branch circuit voltage drop not exceed 3%, with combined feeder and branch not exceeding 5%. This is not code mandatory for most installations, but AHJs treat it as gospel and performance suffers when you ignore it.

The working formula for single phase: VD = (2 x K x I x D) / CM. K is 12.9 for copper, 21.2 for aluminum at 75C. D is one-way distance in feet. CM is circular mils from Chapter 9 Table 8. For three phase, swap the 2 for 1.732.

• 12 AWG copper, 20A load, 100 ft one way: VD = (2 x 12.9 x 20 x 100) / 6530 = 7.9V, or 6.6% on 120V. Fail.
• Bump to 10 AWG (10,380 CM): VD drops to 4.97V, or 4.1%. Still over on branch alone.
• Go to 8 AWG (16,510 CM): VD = 3.12V, or 2.6%. Pass.

On any home run over 75 feet at rated load, upsize one gauge before you pull. Cheaper than a callback and faster than recalculating at the truck.

AC Impedance, Not Just Resistance

Ohm's Law still rules in AC, but R becomes Z (impedance), which combines resistance and reactance. For small conductors in conduit at 60 Hz, resistance dominates. For larger conductors (1/0 and up) or long parallel runs, inductive reactance starts to matter and the simple K factor method underestimates drop.

Chapter 9 Table 9 gives effective Z for AC circuits at 0.85 power factor for conductors in three raceway types. Use it when you're sizing 250 kcmil feeders or running parallel sets. At unity power factor, pull the resistance column and ignore reactance. At heavy motor loads with lagging PF, impedance is noticeably higher than resistance alone.

1. Under 1/0 copper: K factor method is fine.
2. 1/0 and up, or any parallel set: use Table 9 impedance.
3. Motor-heavy loads (below 0.85 PF): derate your calculated ampacity by the PF ratio.

Available Fault Current and Ohm's Law

NEC 110.24 requires service equipment to be field marked with available fault current. You calculate it with Ohm's Law, just at bolted-fault conditions where Z approaches zero.

Starting at the transformer secondary: IFC = (kVA x 1000) / (V x 1.732 x %Z). A 500 kVA, 480V transformer at 5.75% impedance yields roughly 10,460A at the secondary terminals. That's the starting point. From there, conductor impedance on the service and feeder reduces it at each downstream point, which is why the point of use fault current is always lower than at the transformer.

This matters for SCCR compliance under NEC 110.10 and for breaker AIC ratings per 110.9. A 10 kAIC breaker fed by a source with 12 kA available will not clear the fault, it will fail catastrophically.

Always get the utility's available fault current letter before sizing service gear. Assumed numbers get equipment destroyed and inspectors hostile.

Temperature, Ampacity, and the Hidden Ohm's Law Tax

Conductor resistance rises with temperature. NEC 310.15(B) temperature correction factors reflect this, but Ohm's Law explains why. Copper's temperature coefficient is about 0.00393 per degree C. A 90C conductor has roughly 18% more resistance than a 20C conductor. That extra resistance means more voltage drop, more I2R heat, and a feedback loop that can push insulation past its rating.

When you derate for ambient temperature or conductor bundling under 310.15(C)(1), you're really acknowledging that the wire cannot dump heat fast enough, so its equilibrium temperature rises, which raises resistance, which raises heat. Ohm's Law is the mechanism behind the table.

• Attic run in Phoenix (55C ambient): 75C THHN carries only 76% of its 30C rated ampacity per Table 310.15(B)(1)(1).
• Nine current-carrying conductors in one conduit: 70% adjustment per 310.15(C)(1).
• Stack both: effective ampacity is 53% of nameplate. Size up accordingly.

Putting It All Together on a Feeder Calc

Field scenario: 200A, 240V single phase subpanel, 250 feet from service, 80% continuous loading. Per NEC 215.2(A)(1) you need conductors sized for 125% of continuous load, so 250A minimum ampacity. Table 310.16 at 75C column gives 250 kcmil copper.

Check voltage drop: VD = (2 x 12.9 x 200 x 250) / 250,000 = 5.16V, or 2.15% on 240V. Passes the 3% branch recommendation with margin. Now check fault current at the subpanel using Table 9 impedance for 250 kcmil in steel conduit, subtract from source available, verify the subpanel bus and breakers are rated above that number.

Every feeder calc is Ohm's Law applied three times: once for ampacity (thermal), once for voltage drop (performance), once for fault current (safety). Miss any of the three and you've got a job that might pass inspection but will bite someone later.