Mixed calculation practice set

Three weeks before her exam date, Priya sits a timed calculation set at Denise's kitchen table: twelve mixed problems in ninety minutes, code book open, calculator only. It is the last lesson of this course, and it works the same way. Each problem below is the kind of question a Canadian master or contractor exam asks, drawn from the topics of lessons 1 to 11 and set in the jobs you have followed through the course. Try each one before reading the working. Then read the working even if you got it right, because the notes after each problem point out the trap the question was built around.

A reminder for the last time: every value that would come from a Code table is illustrative here and labelled as such. The methods are summarised from the 2024 CE Code Part I. Repeat these problems with your own code book open, replacing the illustrative values with the real ones, and you will have done a genuine exam rehearsal.

How to use a timed set

Denise's method for timed sets is simple. Read every question first and mark each one easy, medium or long. Do the easy ones first, because they bank marks and build confidence. Budget your time by marks: a question worth twice as much gets twice the minutes. Write your working in the same layout every time, so you can check it quickly. When a lookup takes more than two minutes, mark it, move on and come back. And leave ten minutes at the end to do the units, size and direction checks on every answer.

Problem 1: power and resistance

The trap: assuming the current stays the same as on 240 V (22.9 A). With a fixed resistance, a lower voltage means a lower current and much lower power.

Problem 2: three-phase current

The trap: dividing by 600 alone (63.3 A) or by 347 V (109.5 A or 63.2 A depending on the slip). Three-phase uses line-to-line voltage and the square root of three.

Problem 3: a single dwelling

The traps: counting the basement at full area, adding the interlocked air conditioning, and putting the range at 6000 W without the 40% of the excess over 12 kW.

Problem 4: apartment units

The trap: applying the stepped factors to loads that still include heating, which would give a much smaller and wrong answer.

Problem 5: correction factors

The trap: applying the corrections to the 75 °C value (36.4 A) when the insulation allows starting from 90 °C, or stopping at 55 A without corrections.

Problem 6: voltage drop

The trap: forgetting the 2 for single-phase, which halves the drop and makes a conductor that is too small look adequate.

Problem 7: conduit fill

The trap: leaving out the bonding conductor, which would make the total 81 mm², still too big for the smaller conduit here, but in another question it could change the answer.

Problem 8: transformer protection

The trap: using 300% on the primary when there is no secondary protection at 125%.

Problem 9: motors on a feeder

The trap: 125% on all three motors (77.5 A), or adding the largest motor's full-load current instead of its device rating when sizing the feeder device.

Problem 10: overloads

The traps: using 115% because no service factor is marked, and using the table current instead of the nameplate.

Problem 11: adding load to a service

The trap: comparing kVA with amperes, or using 240 V for a three-phase 208 V service.

Problem 12: putting it together

The trap: applying 125% to the whole load (145.7 A) when only part of it is continuous. Read whether the question says the whole load is continuous or only part.

Building your own sets

One timed set is a rehearsal; a dozen are a preparation. The study group writes new sets for each other every week, using the jobs in their own files: a farm shop Marcus wired, a duplex Priya roughed in, a strip-mall unit Tyler helped with. Writing a question is as useful as answering one, because it forces you to decide which conditions matter and where the trap is. Denise's rule for a good practice question is that it should have exactly one trap, stated fairly in the wording, and a single correct answer that a careful reader can reach with the code book and a calculator.

Keep a log of every question you get wrong, with the reason. After a few weeks, the log shows patterns. Priya's showed that most of her misses were continuous-load questions and three-phase single-line loads, so she spent her last two weeks on those. Marcus's showed basement areas and range allowances. Nobody's log showed arithmetic.

After the set

Priya finished in 82 minutes with eleven right. Her one miss was problem 12, where she applied 125% to the whole load. Denise's comment was the one she had made all course: the arithmetic was perfect; the reading was not. On the real exam, Priya underlined every phrase about continuous loads, interlocks, ranges, basements and secondary protection before calculating anything.

That is the habit this course has tried to build. The formulas are few: Ohm's law, power, the square root of three, the voltage drop formula and a handful of multipliers. The tables are in your code book. What earns the marks is reading the question precisely, choosing the right method, writing the working in a consistent layout and checking every answer for units, size and direction.

import math

answers = {
    'P1 hot tub at 208 V (W)': 208**2 / (240**2 / 5500),
    'P2 rooftop unit (A)': 38000 / (math.sqrt(3) * 600),
    'P3 acreage house (A)': (8000 + 16000 + 6400 + 11500 + 0.25 * 10500) / 240,
    'P4 six units (A)': (13500 * 2.95 + 43000 + 9000) / (math.sqrt(3) * 208),
    'P6 max ohms per km': 7.2 * 1000 / (2 * 75 * 60),
    'P8 secondary conductors (A)': 1.25 * 30000 / (math.sqrt(3) * 208),
    'P9 feeder ampacity (A)': 1.25 * 34 + 17 + 11,
    'P12 device (A)': 1.25 * 20000 / (math.sqrt(3) * 208) + 22000 / (math.sqrt(3) * 208),
}
for k, v in answers.items():
    print(f'{k:30s} {v:9.1f}')

P1 hot tub at 208 V (W)           4131.1
P2 rooftop unit (A)                 36.6
P3 acreage house (A)               185.5
P4 six units (A)                   254.9
P6 max ohms per km                   0.8
P8 secondary conductors (A)        104.1
P9 feeder ampacity (A)              70.5
P12 device (A)                     130.5

The script checks the arithmetic of the problems above. Change a value in any line to make your own variation, work it by hand, then run the script to check yourself.