The 2016 October NCEES Electrical PE Exam was described by test takers as strikingly heavy in qualitative theory based questions compared to what was expected.

The large majority of practice material and sample exams focus mostly on quantitative math questions, and this caught many examinees off guard who over prepared for quantitative questions but under prepared for qualitative questions.

To learn from this, let’s talk about the differences between the two main different types of PE exam questions, discuss the best approach to solving qualitative questions, then do an actual step by step demonstration to help you leverage your highest possible score on the exam.

 

Quantitative vs Qualitative

The two main different types of PE exam questions regardless of subject are Quantitative and Qualitative.

 

Quantitative Questions

 

Quantitative questions are math questions. You are given a set of known values that you must use to calculate and solve for an unknown. The purpose of a quantitative question is to test your understanding of how to correctly apply formulas.

An example of a quantitative question would be to:

Determine the apparent power at rated load of a three phase 600 volt 50 horsepower motor using NEC table values for full load amp ratings.

Quantitative questions are what we are most used to preparing for by crunching practice problem after practice problem using reference formulas in individual topics or during a sample exam.

If your weaker area is solving quantitative math problems, then the approach is simple. Focus on solving problems that involve formula based calculations for the given topic.

 

Qualitative Questions

 

Qualitative questions are theory and concept questions and they come in two forms. You are either asked to select the most accurate description from a set given, or you are asked to describe what the result is of changing a specific value or characteristics. The purpose of a qualitative question is to test your knowledge on concepts and theory.

The two different forms you are most likely to see a qualitative question on the PE exam is going to be either a qualitative definition or qualitative relationship.

 

Qualitative Definitions

 

Solving qualitative definition questions successfully depends entirely on two factors. How well you know the subject material the question is based on and how good your references are along with your ability to use them quickly.

An example of a qualitative definition question would be to:

Select the most likely definition for “magnetic flux” or to select the most appropriate reason to conduct a short circuit test.

Qualitative definition questions are simple. You are either sure enough of the definition to wager an answer on, or you need to dig into your reference books to answer.

If you need to start digging through reference books, then we recommend to skip the question and saving it for later by either lightly shading your best guess or leaving it blank.

Once you have finished answering all of the easy questions on the exam first, then you can start using up the valuable remaining time to search for the most appropriate answers for your skipped questions.

This is where having a complete set of references and being familiar with those references is key.

You should know which reference book is most likely to have the answer to the particular question based on the topic. If you have any relevant tabs from studying that match the question then start there, if not skim the index once and write down every applicable keyword and page number so you don’t have to come back to the index. 

Start checking those pages for the keyword and skim the surrounding paragraphs. Move on to the next most appropriate reference book for the given topic if you do not find the answer you are looking for.

 

Qualitative Relationships

 

Solving qualitative relationship questions can be extremely difficult if you do not have much practical hands on experience with the subject matter and have only learned how to solve math based quantitative questions from practice material. This is the focus of this article.

An example of a qualitative relationship question would be to answer:

Which of the following would most nearly result in a decrease of the mechanical torque output of a three phase induction motor:

A) Increase in slip
B) Decrease in rotor speed
C) Decrease in supply voltage
D) Increase in efficiency

We have found that the best way to solve qualitative relationship questions such as these is to look up and write down every formula you can find that fits the question, and then focus on the ones that compare the relationships between the variables in the question. The Goal is to manipulate these formulas until you can derive a relationship that gives a clear answer to what the question is asking for. 

 

Let’s apply this to the above example, and see if we can derive a logical way to select the correct answer for what would most nearly result in a decrease of the mechanical torque output of a three phase induction motor. (The correct answer is C) Decrease in supply voltage):

 

C) Decrease in supply voltage.

Our most basic torque formula relates torque in newton meters to power in watts divided by rotational speed in rpm’s:

According to this, torque is related 1 to 1 with power.

An increase in power will result in an increase in torque by the same factor.

Next, we can relate power to voltage in two major ways:

Since the current a motor draws is depends on the motor resistance, let’s focus on the second one that says power equals the square of the voltage divided by resistance.

This tells us that for every increase in voltage, power increases by the square of the same factor:

Ex: Four times the voltage, or 4V, would result in an increase of power by a factor of (4V)² = 16V!

Let’s plug it into our torque formula for power:

We can now say that torque is related to a factor of the square of the voltage.

This means that decreasing the voltage will decrease the starting power and result in much less torque!

And that C) Decrease in supply voltage is the correct answer.

 

Let’s look at the other possible answers and apply this same type of logic to practice solving qualitative relationships, and to rule out why the other answers cannot be the correct solution to this problem.

 

A) Increase in slip

An increase in slip would actually increase the torque.  Here’s why.

This is the most basic formula for slip:

Let’s re-write it solved for speed, then compare to how it relates to torque:

                           

An increase in slip means a decrease in speed (since slip is negative).

And a decrease in speed results in an increase in torque. Wrong answer.

 

Next possible solution:

B) Decrease in rotor speed

This is an easy one because it is one less step from the previous answer.

We already saw how a decrease in speed results in an increase in torque since speed is the divisor in the torque formula:

   

A decrease in rotor speed results in an increase in torque. Wrong answer.

 

Last possible solution:

D) Increase in efficiency

Efficiency is the ratio of output power to input power:

Input power is the power in watts that the motor draws from the supply current and is constant as long as the load is constant.  Torque is related to a factor of the output power, the power in watts actually doing work on the mechanical load.

So now let’s solve for output power so that we can relate it to the torque formula:

This says that the greater the efficiency (closer to 100% or closer to unity), the more input power is directly translated to output mechanical power, or, the less input power is lost when translated to output power.

 

And according to our torque formula, if power increases because efficiency increases, then torque will increase as well. Wrong answer.

 

That’s it!

Let’s recap:

1. Solve quantitative questions by applying the correct formulas.
2. Solve qualitative definitions by taking the time to become familiar with your references and have enough to cover all topics.
3. Solve qualitative relationships by deriving and substituting applicable formulas and analyzing the subsequent relationships.

 

 

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Comment below and share your experiences and strategy solving quantitative and qualitative Electrical Power questions. Or point out any mistakes you think you may have spotted.

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