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

Ohm's Law, The Field Version

E equals I times R. Voltage equals current times resistance. That one equation, plus the power triangle (P = I x E), covers 90% of the math you actually do on a job site. Everything else is algebra.

Memorize three forms and you are done thinking about it:

• E = I x R (find voltage)
• I = E / R (find current)
• R = E / I (find resistance)

Add the power wheel for loads: P = I x E, P = I² x R, and P = E² / R. If you know any two values, you can solve for the other two. That is the whole trick.

Voltage Drop, The Part That Pays Rent

NEC 210.19(A) Informational Note No. 4 recommends branch circuit voltage drop not exceed 3%, with a combined feeder and branch total not exceeding 5%. It is not a hard code requirement in most cases, but inspectors and engineers treat it like one, and a motor starved for voltage will cook a winding on your warranty.

The field formula for single phase is VD = (2 x K x I x L) / CM, where K is 12.9 for copper, I is load current, L is one way length in feet, and CM is the conductor circular mils from Chapter 9 Table 8. For three phase, swap the 2 for 1.732.

Long run to a well pump or a detached shop? Run the numbers before you pull wire. Upsizing from #12 to #10 on a 120V, 20A, 150 foot run drops you from around 5.8% to 3.6%. Cheaper than a callback.

Sizing Loads With P = I x E

Most nameplates give you watts or VA and a voltage. Divide to get amps, then size the circuit per NEC 210.19 and 210.20. A 1500W space heater on 120V pulls 12.5A. On a 20A circuit that is fine as a single load, but two of them will trip the breaker, and continuous loads need to sit at 80% of the breaker rating per NEC 210.19(A)(1) and 210.20(A).

For motors, forget the nameplate FLA for conductor sizing. Use NEC Table 430.250 (three phase) or 430.248 (single phase) FLC values. Conductors go at 125% of FLC per NEC 430.22, overloads at 115 to 125% of nameplate per 430.32.

Quick field checks that save time:

1. Resistive load on 120V: watts / 120 = amps.
2. Resistive load on 240V: watts / 240 = amps.
3. Three phase motor rough check: HP x 1.25 ≈ FLC amps at 480V.

Series, Parallel, and Why Your Neutral Is Hot

Series circuits share current, voltages add. Parallel circuits share voltage, currents add and resistances combine as 1/Rt = 1/R1 + 1/R2... Lose this and you will misread every troubleshooting call.

A loose neutral on a multiwire branch circuit, NEC 210.4, turns two 120V loads into a series pair across 240V. The load with higher resistance sees more voltage, and LED drivers, electronics, and small appliances start dying in groups. If a customer says "half my kitchen went weird after the dryer ran," that is your first guess.

When you read 208V on a 120V receptacle and 30V on the other leg of the same MWBC, stop. That is an open neutral, not a bad outlet. Kill the circuit before something expensive melts.

Troubleshooting With A Meter And The Law

Ohm's Law turns a meter into a diagnostic tool. Known voltage, measured current, and you can infer the resistance of the load, the condition of a connection, or whether a heating element is open or shorted.

A 4500W water heater element on 240V should read about 12.8 ohms cold (R = E² / P = 57600 / 4500). Read OL and it is open. Read 2 ohms and it is shorted to the sheath. Read 40 ohms and it is degraded, running low and slow.

Voltage drop across a connection under load tells you the resistance of the connection itself. Pull 20A through a lug, measure 2V across it, that lug has 0.1 ohm and is dissipating 40W. It will be hot, discolored, and eventually a callback. NEC 110.14 torque requirements exist for this reason.

Safety Math You Should Not Skip

Body resistance under dry skin contact is roughly 10,000 to 100,000 ohms. Wet or broken skin drops that to 1,000 ohms or less. At 120V and 1,000 ohms, that is 120 mA across your chest, well past the 100 mA ventricular fibrillation threshold.

This is why NEC 210.8 GFCI and 210.8(F) outdoor dwelling GFCI requirements keep expanding, and why 210.12 AFCI exists for arc faults that Ohm's Law alone will not catch. A GFCI trips at 4 to 6 mA in under 25 ms. The math is not on your side without it.

Work it cold when you can, test before touch, and respect that every calculation on your clipboard assumes the conductor is doing what the formula says. Loose terminations, corroded splices, and undersized neutrals break the math in ways that hurt people.