Crash course: Ohm's Law for electricians with calculations (part 1)

Ohm's Law in one line

V = I × R. Voltage equals current times resistance. Every troubleshooting call, every conductor sizing question, every "why is this breaker tripping" starts here. Memorize the wheel or memorize the triangle, but know it cold before you pull wire.

The three forms you will actually use on the job:

• V = I × R (find voltage when you know amps and ohms)
• I = V ÷ R (find current when you know voltage and ohms)
• R = V ÷ I (find resistance when you know voltage and amps)

Power rounds it out: P = V × I. Watts equal volts times amps. Combine the two and you can solve anything on a resistive circuit with two known values.

Reading a circuit like a meter

Voltage is pressure. Current is flow. Resistance is restriction. A 120V circuit feeding a 10 ohm heating element pulls 12 amps (120 ÷ 10 = 12). Drop the resistance to 6 ohms and current jumps to 20 amps. Same voltage, different load, different breaker behavior.

This is why a shorted winding trips a breaker instantly. Resistance collapses toward zero, current spikes, the overcurrent device does its job per NEC 240.4. Keep that mental model when you are chasing nuisance trips.

Field tip: if a motor runs hot and pulls more amps than the nameplate, do not just upsize the breaker. You are masking a mechanical or winding problem, and NEC 430.32 motor overload protection is there for a reason.

Calculation 1: sizing a resistive load

You are installing a 240V baseboard heater rated 1500W. What current does it draw, and what conductor and breaker do you need?

1. I = P ÷ V, so I = 1500 ÷ 240 = 6.25 amps.
2. NEC 424.3(B) requires fixed electric space heating to be treated as a continuous load. Multiply by 125%: 6.25 × 1.25 = 7.81 amps.
3. A 15A breaker with 14 AWG copper handles it per NEC 240.4(D)(3), assuming the terminations and ambient conditions cooperate.

If you parallel a second identical heater on the same circuit, now you are at 15.62 amps continuous. That pushes you to a 20A circuit with 12 AWG, or split the load. Ohm's Law tells you the current. The NEC tells you how to protect it.

Calculation 2: voltage drop on a long run

Voltage drop is Ohm's Law applied to the conductor itself. The wire has resistance, current flows through it, and you lose voltage across that resistance. NEC 210.19(A) Informational Note 4 recommends keeping branch circuit drop at or below 3%, with a total of 5% including the feeder.

Example: 120V, 16A load, 150 feet one way on 12 AWG copper. Resistance of 12 AWG is roughly 1.98 ohms per 1000 feet. Round trip is 300 feet, so total conductor resistance is 0.594 ohms. Voltage drop is V = I × R = 16 × 0.594 = 9.5 volts, or about 7.9%. Too much.

• Bump to 10 AWG (0.99 ohms per 1000 ft): drop = 16 × 0.594 × (0.99 ÷ 1.98) = 4.75 volts, about 3.9%. Better.
• Go to 8 AWG (0.628 ohms per 1000 ft): drop is around 3.0 volts, about 2.5%. Clean.

Long runs cost copper. Calculate before you pull, not after the customer complains their table saw bogs down.

Calculation 3: finding a hidden fault

A customer reports a receptacle that feels warm. You pull it and read 118V line to neutral, but under a 12A load the voltage at the device sags to 104V. What does Ohm's Law tell you?

The drop across the circuit under load is 118 - 104 = 14V. With 12A flowing, R = V ÷ I = 14 ÷ 12 = 1.17 ohms of unexpected resistance. That is not conductor resistance on a normal branch circuit. That is a loose backstab, a corroded splice, or a failing breaker lug. Per NEC 110.14, terminations are torqued to spec for a reason.

Field tip: an IR thermometer or thermal camera will find the hot spot in seconds. Ohm's Law tells you something is wrong. Your eyes and instruments tell you where.

What to memorize before part 2

Part 2 covers AC specifics: power factor, impedance, and how reactive loads break the simple V = I × R model. Before you get there, drill the basics until they are reflex.

1. V = I × R and its two rearrangements.
2. P = V × I and the combined forms (P = I²R, P = V² ÷ R).
3. Continuous load rule: 125% for anything running 3 hours or more, per NEC 210.19(A)(1) and 210.20(A).
4. Voltage drop target: 3% branch, 5% total.
5. Resistance per 1000 ft for 14, 12, 10, and 8 AWG copper. Write them on the inside of your tool bag if you have to.

Ohm's Law does not care what you think the circuit should do. It tells you what it is doing. Trust the math, verify with the meter, and size per the Code.