Crash course: Ohm's Law for electricians with calculations (part 3)

Why Part 3 Matters

Parts 1 and 2 covered the triangle and the power wheel. This one is about the math you actually run on the truck: voltage drop, conductor sizing sanity checks, and load calcs that keep you out of trouble on inspection day.

Ohm's Law does not stop at E = IR. The working form for field electricians is a loop: voltage, current, resistance, and power all feeding each other. If you can move between them without stopping to think, you move faster on every call.

Voltage Drop in the Real World

NEC 210.19(A) Informational Note No. 4 recommends branch circuit voltage drop stay at or below 3%, with a combined feeder and branch drop at or below 5%. It is a recommendation, not a hard rule, but inspectors and engineers treat it as one on spec jobs.

The field formula for single phase: VD = (2 x K x I x D) / CM. K is 12.9 for copper, 21.2 for aluminum. D is one-way distance in feet. CM is the circular mils of the conductor from Chapter 9, Table 8. Three phase uses 1.732 instead of 2.

• #12 THHN copper: 6,530 CM
• #10 THHN copper: 10,380 CM
• #8 THHN copper: 16,510 CM
• #6 THHN copper: 26,240 CM

Worked Example: 120V Branch Circuit

Run a 16 amp continuous load on a 20 amp circuit, 150 feet one way, #12 copper, 120V. VD = (2 x 12.9 x 16 x 150) / 6,530 = 9.48 volts. That is 7.9%. Fail.

Bump to #10: VD = (2 x 12.9 x 16 x 150) / 10,380 = 5.96 volts, about 5%. Still over the 3% branch target. Go to #8: VD = 3.75 volts, about 3.1%. Close enough for most inspectors on a residential feeder, but on a branch you may need #6 or a shorter run.

If the homeowner asks why you are pulling #8 for a 20 amp circuit, tell them the panel is halfway to the next zip code. Distance costs copper.

Using Ohm's Law to Catch Bad Terminations

A loose lug or a corroded splice shows up as added resistance. On a 20 amp load, an extra 0.25 ohms in a connection drops 5 volts and dumps 100 watts of heat into that joint. That is how box fires start.

Quick check in the field: measure voltage under load at the receptacle and at the breaker. The difference is your voltage drop across the run. If the drop is bigger than your calc predicted, something in between is adding resistance. Thermal imaging confirms it fast.

1. Measure unloaded voltage at the outlet.
2. Apply a known load (heat gun, test load bank).
3. Measure loaded voltage at the outlet and at the breaker.
4. Subtract. Compare to your VD calculation.
5. Investigate any gap over 1 to 2 volts.

Sizing a Motor Feeder with Ohm's Law Sanity Check

NEC 430.22 requires motor branch circuit conductors sized at 125% of the motor full load current from Table 430.250. A 10 HP, 230V, three phase motor pulls 28 amps FLC. Conductors at 125% = 35 amps minimum. Table 310.16 at 75C gives #8 copper at 50 amps, plenty.

Now the voltage drop check. 200 feet one way, three phase: VD = (1.732 x 12.9 x 28 x 200) / 16,510 = 7.58 volts, about 3.3% on 230V. Acceptable for most industrial runs, but if the motor is at the end of a long feeder, size up to #6 and keep the drop under 3% so the motor starts cleanly under inrush.

Inrush current on a NEMA Design B motor is six to eight times FLC for a few cycles. If your feeder is marginal on steady state, it will brown out hard on start and trip the contactor.

Power Triangle for Service Calls

P = I x E is the form you use most. A 1500 watt space heater on 120V pulls 12.5 amps. Two of them on the same 20 amp circuit is 25 amps, which is why the breaker keeps tripping. NEC 210.23(A) caps continuous load on a branch circuit at 80% of the rating, so a 20 amp circuit tops out at 16 amps continuous.

For three phase: P = 1.732 x I x E x PF. A 480V three phase load drawing 40 amps at 0.85 power factor = 1.732 x 40 x 480 x 0.85 = 28,263 watts, or roughly 28.3 kW. Useful when a customer hands you a kW rating and asks if their service will carry it.

• Single phase watts: W = V x A x PF
• Three phase watts: W = 1.732 x V x A x PF
• Amps from kW single phase: A = (kW x 1000) / (V x PF)
• Amps from kW three phase: A = (kW x 1000) / (1.732 x V x PF)

Keep These Numbers on the Truck

Print the K values, the circular mils for #14 through 4/0, and the three phase multiplier. Tape them inside the lid of your tool bag. The math is simple once the constants are in front of you.

Ohm's Law is not trivia. It is the fastest way to decide whether a circuit is safe, whether a run is too long, and whether a complaint about "low voltage" is real or a bad neutral. Run the numbers before you pull wire, not after.