Crash course: Voltage, amperage, and resistance basics with calculations (part 4)

Ohm's Law Is the Foundation

Voltage, amperage, and resistance are not abstract. They are the three numbers you balance every time you size a conductor, set a breaker, or chase a nuisance trip. Get the relationship wrong and you waste a service call or burn a lug.

Ohm's Law: E = I x R. Voltage equals current times resistance. Rearrange as needed. I = E / R when you need current. R = E / I when you are calculating impedance from a measured drop. Memorize the triangle, but more importantly, know which variable you actually have in front of you on the truck.

Power follows: P = E x I. Watts equal volts times amps. This is where load calcs live, where you justify a 20A circuit for a 1500W heater, and where you defend your conductor sizing under NEC 210.19 and 215.2.

Voltage: Pressure in the Pipe

Voltage is electrical pressure, the potential difference that pushes electrons. Nominal system voltages are defined in NEC Article 100 and 220.5(A). Use 120, 240, 208, 277, 480 for calculations unless the utility specifies otherwise. Do not calculate with 117 because that is what your meter reads at the receptacle.

Voltage drop is not a code violation under most conditions, but NEC 210.19(A) Informational Note No. 4 and 215.2(A)(1) Informational Note No. 2 recommend a maximum 3% drop on branch circuits and 5% combined on feeders and branches. On long runs, this is what forces you up a wire size before ampacity does.

If you are running a 20A circuit more than about 75 feet on #12 copper at 120V, run the voltage drop math before you pull wire. You will usually be upsizing to #10.

Single phase voltage drop: VD = (2 x K x I x D) / CM. Three phase: VD = (1.732 x K x I x D) / CM. K is 12.9 for copper, 21.2 for aluminum at typical operating temps. CM is circular mils from Chapter 9, Table 8.

Amperage: What Actually Heats the Conductor

Current is what melts insulation, opens breakers, and welds contacts. Ampacity tables in NEC 310.16 are your starting point, but you almost never use the raw number. You apply ambient temperature correction from 310.15(B)(1) and conductor bundling adjustment from 310.15(C)(1) before you compare to your load.

Continuous loads, defined in Article 100 as three hours or more, get sized at 125% per 210.19(A)(1) and 215.2(A)(1). A 16A continuous load needs a 20A circuit and conductors rated for 20A after corrections, not just 16A worth of copper.

• Calculate the load in amps: I = P / E (single phase) or I = P / (E x 1.732) for three phase.
• Multiply continuous portions by 1.25.
• Apply temperature and conduit fill derates to your conductor's table ampacity.
• Pick the next standard breaker size up per 240.6(A), or the next size down if the load is non-continuous and 240.4(B) applies.

Resistance and Why Connections Matter

Resistance opposes current flow and dissipates energy as heat. Conductor resistance is published per 1000 feet in Chapter 9, Table 8 (DC) and Table 9 (AC impedance for typical raceways). Table 9 is what you want for any AC calculation longer than a few feet, because reactance matters on larger conductors.

The resistance you cannot look up is the connection. A loose lug, a backstabbed receptacle, or a corroded splice can add tenths of an ohm where you expect milliohms. At 15A, 0.5 ohms of bad connection dissipates 112 watts inside a wire nut. That is how houses burn.

If a device is warm and the load is normal, the problem is almost always the termination, not the conductor. Pull it, inspect, and re-terminate to the manufacturer's torque spec per 110.14(D).

Working Calculations on the Truck

Most field math is two or three steps. A 240V, 4500W water heater pulls 4500 / 240 = 18.75A. It is continuous, so 18.75 x 1.25 = 23.4A. Minimum 30A breaker per 422.13, #10 copper conductors at the 60C column per 110.14(C)(1)(a) for terminations rated 60C, or at the 75C column if both ends are listed for 75C.

A 208V three phase, 10 HP motor: Table 430.250 gives 30.8A full load. Branch circuit conductors at 125% per 430.22 = 38.5A, so #8 THHN at 75C. Short circuit protection per 430.52 and Table 430.52, inverse time breaker at 250% = 77A, round up to 80A per 240.6(A).

1. Identify the load type: resistive, motor, continuous, or non-continuous.
2. Convert watts or HP to amps using the correct formula.
3. Apply the right NEC multiplier (125% continuous, 125% motor branch, etc.).
4. Size conductor and overcurrent device against the same NEC tables.

What to Carry in Your Head

You do not need to memorize Chapter 9. You need to memorize the relationships and know where to find the tables. E = I x R, P = E x I, 1.732 for three phase, 1.25 for continuous, 60C and 75C termination columns in 110.14(C).

The rest is muscle memory: open the book, find the article, run the number, document it. Voltage, amperage, and resistance are the three knobs the entire code is built around. Once you see every problem as a balance of those three, the calculations stop being a hurdle and start being the fastest way to the right answer.