Crash course: Ohm's Law for electricians with calculations (part 5)

Ohm's Law: The One Equation That Runs the Trade

Voltage, current, resistance. Every calculation you run in the field ties back to these three. V = I × R. Rearrange it two ways and you cover 90% of the math you need on a service call.

The triangle: V on top, I and R on bottom. Cover the one you want, the other two tell you how to get there. V ÷ R = I. V ÷ I = R. I × R = V. Memorize it once, use it forever.

Power rounds it out. P = V × I. Combined with Ohm's Law, you get P = I²R and P = V²/R. These four equations solve almost every sizing, troubleshooting, and load question you'll hit on a residential or light commercial job.

Sizing a Branch Circuit: Worked Example

Customer wants a 1500W space heater on a dedicated 120V circuit. What's the load in amps, and what breaker and conductor do you pull?

I = P ÷ V = 1500 ÷ 120 = 12.5A. That's the continuous load. NEC 210.19(A)(1) and 210.20(A) require conductors and overcurrent protection sized at 125% of continuous load: 12.5 × 1.25 = 15.6A. Round up to a 20A breaker with #12 THHN copper. Never a 15A breaker. Heaters run for hours and that 80% rule isn't optional.

Field tip: if the nameplate lists watts and volts but not amps, do the division before you leave the truck. Saves a second trip when you realize the existing 15A circuit won't cut it.

Voltage Drop: Where Ohm's Law Bites You

Long runs kill voltage. NEC 210.19(A) Informational Note No. 4 recommends branch circuit voltage drop not exceed 3%, with total drop (feeder plus branch) capped at 5%. It's not mandatory, but inspectors and smart electricians treat it like it is.

Single-phase voltage drop formula: VD = (2 × K × I × D) ÷ CM. K = 12.9 for copper, 21.2 for aluminum. D is one-way distance in feet. CM is circular mils from NEC Chapter 9, Table 8.

Example: 20A load, 150 feet, #12 copper (6530 CM). VD = (2 × 12.9 × 20 × 150) ÷ 6530 = 11.85V. On a 120V circuit that's 9.9% drop. Way out of spec. Bump to #10 (10380 CM) and you get 7.45V, or 6.2%. Still too high. Go to #8 and you land inside 3%. This is why long garage and barn feeds almost always need upsized conductors.

• Under 50 feet on a 20A circuit: #12 is usually fine.
• 50 to 100 feet: check the math, often #10.
• Over 100 feet: assume upsize, verify with calculation.

Troubleshooting with Ohm's Law

A circuit trips immediately when energized. You suspect a ground fault or short. Pull the load, meter resistance across the conductors. A healthy 15A circuit with nothing connected should read open (OL) or very high megohms to ground. A reading of 2 ohms between hot and ground means I = 120 ÷ 2 = 60A of fault current. That's your trip.

Running motor warm? Measure voltage at the motor under load. If a 240V motor is reading 220V, you've lost 20V somewhere. I on the nameplate is 15A. R of the lost path = 20 ÷ 15 = 1.33 ohms. That's a loose lug, a corroded splice, or an undersized conductor. Ohm's Law points you at the problem before you start pulling devices.

Field tip: always take voltage readings under load, not open circuit. A failing connection hides at no load and shows itself the moment current flows.

Three-Phase Math for Commercial Work

Three-phase changes the power equation: P = V × I × √3 × PF. √3 is 1.732. Power factor is typically 0.85 to 1.0 for resistive and motor loads. Forget the √3 on three-phase and your conductor sizing will be off by 73%.

Example: 50 HP three-phase motor at 480V. NEC 430.250 gives the FLC directly, but if you're verifying: P = 50 × 746 = 37,300W at unity. Real world at 0.88 PF and 91% efficiency, input is roughly 46,580W. I = 46,580 ÷ (480 × 1.732 × 0.88) = 63.7A. Cross-check against Table 430.250, which lists 65A. Close enough to confirm your meter and your math.

• Always use NEC 430.250 tables for motor FLC, not nameplate, per NEC 430.6(A)(1).
• Size conductors at 125% of FLC: NEC 430.22.
• Size overload protection from nameplate: NEC 430.32.

Quick Reference You Can Use Tomorrow

Keep these in your head. They cover the vast majority of residential and light commercial calls.

1. Amps from watts: I = W ÷ V (single-phase).
2. Amps from watts, three-phase: I = W ÷ (V × 1.732 × PF).
3. Continuous load sizing: multiply by 1.25 (NEC 210.20(A), 215.3).
4. Voltage drop, single-phase: VD = (2 × K × I × D) ÷ CM.
5. Power dissipation in a conductor: P = I²R. This is why loose connections burn.

The math doesn't lie and it doesn't care how long you've been in the trade. Run the numbers, size the wire, pull the right breaker. The code catches what Ohm's Law predicts, every time.