Crash course: Ohm's Law for electricians with calculations (part 2)

Power, Not Just Voltage and Current

Part 1 covered V = IR. Part 2 gets into power, voltage drop, and the math you actually run on the job. Power is where Ohm's Law earns its keep because everything you size, breakers, conductors, overloads, traces back to watts.

The power wheel gives you three forms: P = VI, P = I²R, and P = V²/R. Pick whichever matches the values you have. On a service call you rarely get all four variables handed to you, so knowing all three forms saves time.

Example: a 240V baseboard heater pulling 12.5A. P = VI = 240 × 12.5 = 3000W. That lines up with the nameplate, confirms the circuit is loaded as designed, and tells you a 20A breaker on #12 THHN is correct per NEC 210.19 and 240.4(D).

Voltage Drop: The Calculation Inspectors Actually Check

NEC 210.19(A) Informational Note No. 4 recommends branch circuits be sized so voltage drop does not exceed 3%, with combined feeder and branch circuit drop capped at 5%. It is not a hard code requirement, but it is a design standard and inspectors flag it on long runs.

Single-phase voltage drop formula: VD = (2 × K × I × L) / CM. K is 12.9 for copper, 21.2 for aluminum. L is one-way length in feet. CM is the conductor's circular mil area from NEC Chapter 9, Table 8.

Run the numbers before you pull wire on anything over 100 feet. A 20A circuit on #12 copper pulling 16A at 150 feet one-way drops: (2 × 12.9 × 16 × 150) / 6530 = 9.48V. That is 7.9% on a 120V circuit, way over limit. Upsize to #10 and you drop to 6.0V, or 5%. Still marginal. #8 brings it to 3.75V, 3.1%.

Sizing Conductors with Ohm's Law Logic

NEC 310.16 gives you ampacity based on insulation type and conditions of use. Ohm's Law tells you what current the load will actually pull, which sets the minimum ampacity before you apply adjustment factors.

For continuous loads, NEC 210.19(A)(1) and 215.2(A)(1) require conductors sized at 125% of the continuous load current. A 40A continuous load needs conductors rated for at least 50A. Run I = P/V first, identify continuous versus non-continuous, then apply the multiplier.

• Non-continuous load: conductor ampacity ≥ load current
• Continuous load (3 hours or more): conductor ampacity ≥ 125% of load current
• Mixed: 125% of continuous + 100% of non-continuous
• Apply derating from NEC 310.15(C)(1) for more than 3 CCCs in a raceway
• Apply ambient correction from NEC 310.15(B) when temperature exceeds 30°C

Motor loads do not follow the 125% continuous rule the same way. NEC Article 430 uses FLC from Tables 430.247 through 430.250, not nameplate, and branch circuit conductors are sized at 125% of table FLC per 430.22. Do not mix up the rules.

Power Dissipation and Heat

P = I²R is the form that tells you why loose connections burn up panels. Resistance at a bad termination might be 0.1 ohm instead of 0.001 ohm. At 30A, that is 0.1 × 900 = 90W dissipated at a single lug. That is a soldering iron inside your panel.

This is also why NEC 110.14(D) now requires torque specs on terminations. The code is chasing a physical reality: power dissipation scales with the square of current, so any added resistance at high current turns into destructive heat fast.

When troubleshooting a nuisance trip or a hot breaker, think I²R. Measure voltage drop across the termination under load with a low-range DMM. A reading above 0.5V across a lug at rated current means you have resistance that needs to go.

Three-Phase and Line-to-Line Math

Three-phase power uses P = √3 × VL × IL × PF for balanced loads. The √3 factor (1.732) trips up apprentices. It comes from the geometry of phase relationships, not anything you need to derive on the job, just memorize it.

A 480V, 3-phase, 100A load at 0.85 PF: P = 1.732 × 480 × 100 × 0.85 = 70,646W, or roughly 70.6 kW. Going the other direction, sizing a feeder for a 75 kW load at 480V 3-phase, 0.9 PF: I = P / (√3 × V × PF) = 75,000 / (1.732 × 480 × 0.9) = 100.2A.

For three-phase voltage drop, the formula changes to VD = (√3 × K × I × L) / CM. Half the drop of single-phase for the same conductor and load, because the return path is shared across phases.

Field Checks That Use the Math

Ohm's Law is not just design work. It is your troubleshooting framework. When something does not add up, the math tells you where to look.

1. Measure voltage at the source and at the load under full current. The difference is your total voltage drop, including every connection.
2. Divide measured VD by measured current to get total circuit resistance. Compare to calculated conductor resistance from Chapter 9 Table 8. Excess is in connections.
3. On a motor drawing more than nameplate FLA, check voltage first. Low voltage forces higher current for the same mechanical load per P = VI.
4. For a breaker tripping below rated load, measure actual current with a clamp meter before assuming the breaker is bad. Harmonics and inrush count.

Keep a laminated card in your truck with the three power formulas, the single-phase and three-phase voltage drop formulas, and the K values for copper and aluminum. You will reach for it more than any app.