# Practice problem worksheets

NEW: I am developing a new set of open-source learning modules on electricity and electronics. This is called the ModEL Project, with each module being a self-contained document complete with introduction, review, tutorial, question sets, and projects/experiments. Like everything on this website, all ModEL Project documents and files are "copylefted" under a Creative Commons Attribution-Only license.

### Mathematics

• Fractions (this worksheet helps teach and reinforce concepts necessary to perform simple arithmetic with fractions.)
• Fundamental principles of algebra (this worksheet helps teach and reinforce concepts necessary to manipulate and substitute algebraic equations.)
• Applications of trigonometry (this worksheet helps teach and reinforce concepts necessary to apply right-triangle trigonometry to the solution of practical problems.)
• Calculus concepts and applications (this worksheet helps teach and reinforce concepts related to differentiation and integration, mostly qualitative and numerical as opposed to symbolic.)

### Electricity and Electronics

• Voltage, Current, Resistance, and Basic Circuit Concepts, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you the basic principles of electricity and electric circuits. I recommend all students struggling with circuit analysis to begin with this learning module, as it endeavors to clear many common misconceptions of electricity. The basis of this entire learning module series is an emphasis on "first principles" of physics, especially the Laws of Energy, Charge, and Mass conservation.
• Sources and Loads, Voltmeters and Ammeters, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you how to view electric circuit components as either sources of energy or loads of energy. These concepts are extremely helpful in circuit analysis, as well as in circuit design and interconnections between components.
• Ohm's and Joule's Laws, Resistor Ratings, and Electrical Safety, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you Ohm's and Joule's Laws as they relate to simple circuits. These concepts serve well as preludes to the important topic of electrical safety.
• Diagnostic Fundamentals, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you how to scientifically diagnose basic circuit faults (opens and shorts).
• Series DC circuits, from the Socratic Electronics project. This worksheet helps teach the concepts of series electrical circuits using DC power sources.
• Series Circuits and Voltage Dividers, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you how to analyze series DC circuits. Like all the other ModEL learning modules, this one stongly emphasizes "first principles" of Energy and Charge Conservation as a basis for understanding voltage, current, and resistance in circuits.
• Parallel DC circuits, from the Socratic Electronics project. This worksheet helps teach the concepts of parallel electrical circuits using DC power sources.
• Parallel Circuits and Current Dividers, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you how to analyze parallel DC circuits. Like all the other ModEL learning modules, this one stongly emphasizes "first principles" of Energy and Charge Conservation as a basis for understanding voltage, current, and resistance in circuits.
• Kirchhoff's Laws, from the Socratic Electronics project. This worksheet helps teach the concepts of Kirchhoff's Voltage and Current Laws as they apply to electrical circuits using DC power sources.
• Kirchhoff's Voltage Law, from the ModEL Project. This document contains a complete tutorial and problem sets designed to explain KVL and how to apply it to simple circuits. Like all the other ModEL learning modules, this one stongly emphasizes "first principles" of Energy and Charge Conservation as a basis for understanding all electrical concepts.
• Kirchhoff's Current Law, from the ModEL Project. This document contains a complete tutorial and problem sets designed to explain KCL and how to apply it to simple circuits. Like all the other ModEL learning modules, this one stongly emphasizes "first principles" of Energy and Charge Conservation as a basis for understanding all electrical concepts.
• Series-parallel DC circuits, from the Socratic Electronics project. This worksheet helps teach the concepts of series-parallel combination electrical circuits using DC power sources.
• Series-Parallel Circuits, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you how to analyze series-parallel DC circuits. Like all the other ModEL learning modules, this one stongly emphasizes "first principles" of Energy and Charge Conservation as a basis for understanding voltage, current, and resistance in circuits.
• Qualitative Circuit Analysis, from the ModEL Project. This document contains a complete tutorial and problem sets designed to teach you how to analyze simple circuits without using any mathematical calculations. Like all the other ModEL learning modules, this one stongly emphasizes "first principles" of Energy and Charge Conservation as a basis for understanding voltage, current, and resistance in circuits.
• DC bridge circuits, from the Socratic Electronics project. This worksheet helps teach the concepts of Wheatstone bridge circuits using DC power sources.
• DC circuit calculations
• Transformer circuit calculations
• AC reactive circuit calculations
• Process switches and switch circuits
• Process switches and PLC circuits (this worksheet helps teach and reinforce concepts of normally-open and normally-closed contacts, both real and virtual, and how their statuses relate to each other. This happens to be one of the more challenging concepts to master when learning PLC ladder-diagram programming.)
• Pictorial circuit diagrams (this worksheet helps teach and reinforce concepts of wiring components together that are not drawn in neat, organized, schematic form -- an essential concept to master for performing actual device wiring on the job!)
• Basic circuit troubleshooting, from the Socratic Electronics project. This worksheet helps teach the effects of open connections in simple DC circuits, especially with regard to the presence or absence of voltage between specified test points.
• Basic troubleshooting strategies, from the Socratic Electronics project. This worksheet helps teach effective diagnostic strategies applicable to electrical circuits as well as other systems.
• Fault analysis of simple circuits (this worksheet helps teach how to assess the likelihood of different faults in simple electrical circuits -- an essential concept to master for performing troubleshooting on the job!)
• Three-phase AC circuits (this worksheet helps teach how to calculate voltage, current, and power quantities in three-phase AC circuits)

### A collection of realistic instrumentation diagrams

While not a practice-problem worksheet in the strictest sense, this worksheet nevertheless contains a set of useful P\&ID and loop diagrams drawn with industry-realistic levels of detail. These are helpful for students wishing to gain more experience interpreting and drawing such diagrams, as well as instructors who might wish to take these diagrams and use them as the basis for homework or exam questions.

As with all the diagrams in the Socratic Instrumentation project, these graphic images are vector-based, not raster, and as such may be magnified without pixellation.

### Sample mastery exam

Mastery exams are administered repeatedly throughout the second year of the Instrumentation program to ensure learning on a variety of essential topics. A 100% (perfect) score is necessary to pass. Failure to attain 100% correctness on a mastery exam results in re-taking another version of the mastery exam in its entirety. There is no grade penalty for any number of re-takes, but the student must pass the mastery exam by a specified deadline date in order to pass the course.

The way a mastery exam is administered is like this: the student takes the exam, presents it live to the instructor, who then grades it against an answer sheet (see the last page, not printed for students). If 100% of the answers are correct, the student passes the exam. If any answers are incorrect and/or if any work is not shown, the instuctor then marks which section(s) of the exam contain mistakes on the table at the top of the cover page and hands the exam back to the student, who now has one more chance to review their work and correct any errors. No hints whatsoever are given to the student regarding the mistakes or omissions. If upon the student's second submission all answers are 100% correct, the student passes the exam. If, however, any old mistakes remain and/or any new mistakes have been made, the student then must meet with the instructor to determine where they went wrong, what they should practice or study more, and when the re-test will be (with a different version of the exam).

The following links provide samples of a mastery exam designed to test knowledge on a variety of first-year (basic electricity and electronics) concepts:

### Certification Prep exams

These are multiple-choice exams written in the same style as popular certification exams, designed to cover most of what a typical two-year program in Instrumentation would teach. Admittedly, these ``certification prep'' exams are much less rigorous than typical exams given in the Instrumentation program, but they are good practice for employment entrance exams and industry-recognized certification exams, which sadly tend to focus more on rote memorization and recognition rather than actual problem-solving skill. I no longer give this exam as practice to my students, and so the answers to all questions are provided on the last several pages of each exam so that you may check your own performance: