Ohm's Law and Power Formulas for the Electrician Exam

The four relationships

Ohm's law ties voltage, current and resistance together. The power formula ties power to voltage and current. In symbols:

• Voltage = current × resistance (V = I × R)
• Power = voltage × current (P = V × I)

Substitute one into the other and you get two more forms that save a step when you know resistance:

• P = I² × R
• P = V² ÷ R

That is the whole set for DC and for single-phase resistive loads. For anything where you know two quantities, one of the four gives you a third without a detour. Write the formula first, then the numbers with their units, then the answer. The order matters because a wrong option on this kind of item is usually the right formula with a slipped unit.

Worked example: find the current

A resistive heater draws 4,800 watts from a 240 volt single-phase supply. What is the current? Rearrange P = V × I to I = P ÷ V: 4,800 ÷ 240 = 20 A. Check: 240 × 20 = 4,800 W. If you had used 120 V by mistake you would get 40 A, which is exactly the wrong option an exam writer would offer.

Worked example: find the resistance

A load draws 12 A from a 120 volt supply. R = V ÷ I = 120 ÷ 12 = 10 ohms. Power is 120 × 12 = 1,440 W, and you can confirm it with I² × R: 144 × 10 = 1,440 W. Using a second form to verify costs five seconds and catches most slips.

Three-phase power

For a balanced three-phase load, apparent power uses the line voltage, the line current and the square root of 3, which is about 1.732. Real power adds the power factor.

• Apparent power in volt-amperes = 1.732 × line voltage × line current
• Real power in watts = 1.732 × line voltage × line current × power factor

Worked example: a three-phase, 208 volt load draws 30 A at a power factor of 0.9. Apparent power is 1.732 × 208 × 30 = about 10,808 VA. Real power is that times 0.9, which is about 9,727 W. Many wrong options come from using 3 instead of 1.732, or from forgetting the power factor, so write the factor in the formula before you enter anything.

Series and parallel in two lines

In series, resistances add and the current is the same through each. In parallel, the voltage is the same across each branch and the currents add. Two equal resistors in parallel give half of one. When the question gives you three unequal parallel resistors, the reciprocal method works: the reciprocal of the total is the sum of the reciprocals. Do the sum in your calculator and invert at the end.

Keep theory separate from code values

Theory items do not ask you to look anything up, and calculations that do use the NEC send you to a table by article number, as our calculations portion guide shows. When a question mixes the two, such as a load current feeding an ampacity step, do the theory first and carry the current forward with its units. For voltage drop, theory gives you the drop in volts and the NEC's informational notes give the usual percentage targets. See our voltage drop guide.

Drill it until it is automatic

The way to make these reflexes is repetition on varied numbers. The Ohm's law calculator lets you enter any two of voltage, current, resistance and power and see the rest, with three-phase and power factor included. Work each problem by hand first, then use the calculator to check yourself. Use the same non-programmable calculator you will carry on exam day, because key order differs between models.

See where you stand

Theory is only one of ten subject areas. Take the free 10-question check to see your score across all ten, with each answer explained, no signup needed.

FAQ

Do I need to memorize Ohm's law for the Texas journeyman exam?

Plan to. Ohm's law and the power formulas are not NEC text, so know them cold. Your own notes made in your NEC before the exam are allowed, but a page of formulas is slower than knowing them.

What is the square root of 3 used for?

It converts a line value to a three-phase total. Use 1.732 in three-phase power calculations.