Checked against primary sources 2026-08-24

You will not be asked to state it. You will be asked to use it under pressure.

Five scored items on the journeyman paper carry a theory label. The relationship behind them sits inside a great many more, which is why speed here buys time everywhere else.

The relationship

Voltage equals current times resistance. Rearrange that one sentence and you have the current, or the resistance, and that is most of what a theory item asks you for.

Volts times amperes gives volt-amperes. It gives watts only when the load is resistive, meaning a heater, an incandescent lamp, anything with no motor and no transformer in it. Keep that qualifier attached and the twelve-form power wheel is useful. Drop it and the wheel quietly hands you the wrong unit.

Work it once with numbers you can check. Put 240 volts across 12 ohms and the current is 20 amperes, because 240 divided by 12 is 20. Power is 240 times 20, or 4800 watts. Square the current and multiply by the resistance: 400 times 12 is 4800. Square the voltage and divide by the resistance: 57,600 over 12 is 4800.

Three forms, one answer. That agreement is your check, and it costs about ten seconds.

The rearrangements you actually use

• Current from voltage and resistance: divide the voltage by the resistance.
• Current from power and voltage: divide the power by the voltage.
• Power from current and resistance: square the current, then multiply by the resistance.
• Power from voltage and resistance: square the voltage, then divide by the resistance.

The last two are the ones people reach for a chart to find. Both fall out of substituting one relationship into the other, and both hold for a resistance. Do not aim either at a motor, where the current is set by impedance and phase angle rather than by a resistance you can look up.

A 1500 watt heater on 120 volts draws 12.5 amperes and behaves like 9.6 ohms. Check it backward: 120 squared is 14,400, divided by 9.6 is 1500. If your two routes to the same quantity disagree, one of them has a slipped decimal in it and you have found the slip before you marked the answer.

Where volt-amperes and watts diverge

On a resistive load they are the same number, which is why the distinction feels academic right up to the first motor question.

On a motor or a transformer they are not, because the current and the voltage are out of step with each other. The load calculation rules in the code are written in volt-amperes, so the answer does not depend on what the power factor of the connected equipment turns out to be.

An item that hands you a power factor wants the conversion, and it is telling you so by handing it to you. An item that does not hand you one is not inviting you to assume a value. It might not be an arithmetic item at all: horsepower and a voltage with no power factor is a motor item, and those are answered from a full-load current table.

Three-phase, and where the square root of three actually goes

The factor lives on the boundary between line quantities and phase quantities. Cross that boundary and it appears. Stay on one side of it and it does not.

• Wye: line-to-line voltage is the square root of three times the line-to-neutral voltage. Line current is the phase current, unchanged.
• Delta: line current is the square root of three times the phase current. Line voltage is the phase voltage, unchanged.
• Total apparent power, either connection: the square root of three times line voltage times line current, which is the same quantity as three times phase voltage times phase current.

Check the two power forms against each other on a 208Y/120 system carrying 30 amperes per line. The line form gives 1.732 times 208 times 30, or 10,808 volt-amperes. The phase form gives 3 times 120 times 30, or 10,800. They agree, and the small gap is 208 being the rounded name for the square root of three times 120.

Three slips come out of this and each has its own signature. Leave the factor out of the line form and you are low by about 1.73. Use 3 where the square root of three belongs and you are high by that same 1.73. Work per phase and forget to multiply by three and you are low by 3.

What this is worth on the paper

Five scored items on the journeyman exam, and the machinery inside a good many more.

The testing vendor publishes a content outline for each portion. On the journeyman knowledge portion, Definitions, Theory, and Plans carries 3 of the 56 scored items. On the journeyman calculations portion, Calculations and Theory carries 2 of the 24. A master candidate gets 7 of 70 and 2 of 30.

So the direct return is small and the indirect return is not, because every load calculation ends in an ampere figure and the last step of getting there is this relationship. Drill it for speed rather than for understanding. The understanding is already yours. The clock is not.

What this page cites

• PSI Candidate Information Bulletin, TDLR Electricians Updated 9 July 2026. Publishes the content outline for each portion, including the theory item counts quoted above, and the item and time limits they sit inside. source