10 problems, all seven types in every set. Work each one before you open its steps.
Problem 1: Voltage drop
A 480 V three-phase circuit carries 70 A to a load 175 ft away (one way). The copper conductors are 2 AWG, 66,371 circular mils. Use K = 12.9 Ω·cmil/ft. What is the voltage drop as a percentage of the source voltage?
Show the answer and steps
Answer: 0.86%
- Three-phase: VD = 1.732 × K × I × L ÷ cmil, with L the one-way length.
- VD = 1.732 × 12.9 × 70 × 175 ÷ 66,371 = 4.12 V.
- Percent drop = 4.12 ÷ 480 × 100 = 0.86%.
Problem 2: Ohm's law
A heating element of 6 Ω carries 12 A. How much power does it use, in watts?
Show the answer and steps
Answer: 864 W
- With current and resistance known, use P = I² × R and skip the voltage step.
- P = 12² × 6 = 144 × 6 = 864 W.
- Check with E × I: E = 12 × 6 = 72 V, and 72 × 12 = 864 W.
Problem 3: Continuous load at 125%
A branch circuit serves 27 A of continuous load and 8 A of noncontinuous load. What minimum ampere rating does the 125% rule give, before rounding up to a standard size?
Show the answer and steps
Answer: 41.75 A
- Continuous part at 125%: 27 × 1.25 = 33.75 A.
- Add the noncontinuous part at 100%: 33.75 + 8 = 41.75 A.
- In 2023 NEC numbering the rule is at 210.19(A)(1) for the conductor and 210.20(A) for the overcurrent device; confirm the numbers in your 2026 book. Rounding up to a standard device rating is a separate step this drill leaves out.
Problem 4: Transformer full-load current
A 45 kVA three-phase transformer has a 240 V line-to-line winding. What is the full-load line current on that side, in amperes?
Show the answer and steps
Answer: 108.25 A
- Three-phase: I = kVA × 1,000 ÷ (1.732 × E).
- 1.732 × 240 = 415.68.
- I = 45,000 ÷ 415.68 = 108.26 A.
- With the exact square root of 3 the key prints as 108.25 A. Both are inside the self-check tolerance.
- Dividing by 3 in place of 1.732 gives a current that is far too small.
Problem 5: Series and parallel resistance
A 2 Ω resistor is in series with a parallel pair of 24 Ω and 24 Ω, across a 24 V source. What is the total current, in amperes?
Show the answer and steps
Answer: 1.71 A
- Reduce the pair first, product over sum: (24 × 24) ÷ (24 + 24) = 12 Ω.
- Add the series resistor: 2 + 12 = 14 Ω.
- Ohm's law: I = 24 ÷ 14 = 1.71 A.
Problem 6: Three-phase power
A balanced three-phase load on 240 V line-to-line draws 15 A per line at a power factor of 0.9. What is its true power, in watts?
Show the answer and steps
Answer: 5,612 W
- Three-phase true power: P = 1.732 × E × I × PF, with line voltage and line current.
- Apparent power: 1.732 × 240 × 15 = 6,235 VA.
- True power: 6,235 × 0.9 = 5,612 W.
- The common miss is using 3 in place of 1.732, or leaving out the power factor.
Problem 7: Single-phase power
A single-phase load uses 1,800 W of true power on 240 V at a power factor of 0.95. What current does it draw, in amperes?
Show the answer and steps
Answer: 7.89 A
- Rearrange P = E × I × PF for current: I = P ÷ (E × PF).
- E × PF = 240 × 0.95 = 228.
- I = 1,800 ÷ 228 = 7.89 A.
- Sanity check: a power factor below 1 always means more current than P ÷ E alone.
Problem 8: Continuous load at 125%
A branch circuit serves 12 A of continuous load and 10 A of noncontinuous load. What minimum ampere rating does the 125% rule give, before rounding up to a standard size?
Show the answer and steps
Answer: 25 A
- Continuous part at 125%: 12 × 1.25 = 15 A.
- Add the noncontinuous part at 100%: 15 + 10 = 25 A.
- In 2023 NEC numbering the rule is at 210.19(A)(1) for the conductor and 210.20(A) for the overcurrent device; confirm the numbers in your 2026 book. Rounding up to a standard device rating is a separate step this drill leaves out.
Problem 9: Three-phase power
A balanced three-phase load on 480 V line-to-line draws 60 A per line at a power factor of 0.85. What is its true power, in watts?
Show the answer and steps
Answer: 42,401 W
- Three-phase true power: P = 1.732 × E × I × PF, with line voltage and line current.
- Apparent power: 1.732 × 480 × 60 = 49,882 VA.
- True power: 49,882 × 0.85 = 42,399 W.
- With the exact square root of 3 the key prints as 42,401 W. Both are inside the self-check tolerance.
- The common miss is using 3 in place of 1.732, or leaving out the power factor.
Problem 10: Ohm's law
A 240 V source feeds a resistive load of 48 Ω. What current does the load draw, in amperes?
Show the answer and steps
Answer: 5 A
- Ohm's law solved for current: I = E ÷ R.
- I = 240 ÷ 48 = 5 A.
- Check it back: 5 × 48 = 240 V.
Score yourself
Give yourself one point for each answer within 0.5% of the key. That leaves room for 1.732 against the exact square root of 3 and for rounding once at the end. Rework every miss by hand from its steps before you start the next set.
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How the practice set works
Each set has 10 problems. The first seven cover every type once in a shuffled order, and the last three repeat types at random. Every problem gives you all its numbers, so you need a calculator and nothing else. Open Show the answer and steps only after you have an answer written down.
The set number at the top picks the numbers. The same set number always gives the same ten problems, so quote it with the problem number if you report an error. New set moves to the next set number.
The formulas behind each type
- Ohm's law. E = I × R, with P = I² × R and P = E² ÷ R when resistance is known.
- Single-phase power. P = E × I × PF. E × I alone is apparent power in volt-amperes.
- Three-phase power. P = 1.732 × E × I × PF, with line-to-line voltage and line current.
- Transformer full-load current. I = kVA × 1,000 ÷ E for single-phase, and kVA × 1,000 ÷ (1.732 × E) for three-phase.
- Voltage drop. VD = 2 × K × I × L ÷ cmil for single-phase and 1.732 × K × I × L ÷ cmil for three-phase, with L the one-way length. K and the circular mils are given in each problem.
- Series and parallel resistance. Series resistances add. In parallel, the reciprocal of the total is the sum of the reciprocals.
- Continuous load at 125%. 1.25 × the continuous load plus the noncontinuous load gives the minimum before you round up to a standard rating. The rule is at 210.19(A)(1) and 210.20(A) in 2023 numbering, so confirm the numbers in your 2026 book.
The first six are standard physics in our own words. The method for the table-driven calculations, by NEC article and table number, is in the Calculations portion guide, and the master Calculations guide works the longer version.
Worked example: a three-phase line current
A balanced 30 kW load runs on 480 V, three-phase, at a power factor of 0.9. Step 1: convert to watts, 30 × 1,000 = 30,000 W. Step 2: the divisor, 1.732 × 480 × 0.9 = 748.22. Step 3: I = 30,000 ÷ 748.22 = 40.09 A. Leaving out the power factor gives 36.09 A, and using 3 in place of 1.732 gives 23.15 A. Both are the kind of wrong option a careful setup avoids. This is an original example, not an exam question.
Calculations practice FAQ
Where do these practice problems come from?
Every problem is original and written to the published PSI outline for the Texas electrician exams, which lists Calculations and Theory, Transformers and Branch Circuit Calculations in the Calculations portion. The numbers are made up and drawn from a seed, and every key comes from the same math as the calculators on this site.
Why are there no ampacity, motor or conduit fill problems?
Those answers come from NEC tables, and we never reproduce code-book values. Every problem here gives you all its inputs, including K and circular mils for voltage drop. Work the table problems from your own NEC with the method in our Calculations portion guide.
Does this help with the Texas master electrician exam too?
Yes. The PSI outline lists Calculations and Theory, Transformers and Branch Circuit Calculations in the master Calculations portion as well, and these formulas are the same at both levels. The master portion adds more service and motor work, which needs your NEC tables.
What calculator can I bring to the exam?
PSI allows only non-programmable calculators that are silent, battery-operated, have no paper tape printing and have no alphabet keyboard. Practice these sets on the calculator you will carry, so the key order is familiar.