Simplify Parallel Calculations

The total resistance in a parallel circuit is difficult to calculate because it cannot simply be added as in a series circuit. However, the total current flow in a parallel circuit is easy to calculate. It is simply the sum of the currents for all the individual loads. The famous parallel formula for resistances in parallel uses this concept.  Dividing the resistance of each load into 1 calculates the current draw for each load at 1 volt. Adding these fractions gives the total current draw of the entire circuit at 1 volt. Since resistance can be calculated by dividing current into voltage, dividing the total circuit current at 1 volt into 1 volt gives the total resistance. I confess that I have used and taught this formula for many years without knowing why it works. Once I understood the reason behind the formula, it seemed far more logical and less imposing.  Did you know that this works for any voltage you choose? We can use this to create a simpler parallel calculation. 


I find that many of today’s digital students struggle with the fractions, common denominators, and all the trappings that go with fractions. One solution is to convert the fractions to decimals. But the decimal numbers you get when dividing whole numbers into one are always several decimal places to the right of 0, causing another own sort of confusion. My suggestion is to choose a voltage at least equal to the highest resistance; preferably, twice the highest resistance. That way, all the answers will have at least one whole number. This not only makes the answers easier for the students to deal with, it makes the decimals to the right of 0 less significant, so lopping off a few won’t have as big an impact on the final answer.


 For example, with resistances of 15, 20, and 30 ohms choose 60 volts. Instead of trying to add 1/15  + 1/20 + 1/30  or their decimal equivalents, you are adding 60/30 + 60/20 + 60/15. Most people can add 2 + 3 + 4. Then, divide this total current, 9 amps, into the voltage we used, 60 volts, to get 6.6 ohms total resistance. OK, so I stacked the deck a bit. Another teacher’s trick – if you get to choose the questions, why not choose questions that make your life easier. After your students are adept at these “easy” problems, have them measure the resistance of some actual devices and do the calculations. This is where choosing to make the calculations easier really pays off. Anybody can make simple things difficult – the trick to teaching is to make difficult things simple. 

A Story of Personal Courage

Have you ever wondered how you would react in the face of personal tragedy? I have. When I read about tragedies in the paper or hear about them on the news, I find myself wondering “What if..?”  Fortunately, I have never found out. Soon the business of the day drowns out my musings, and I return to the business at hand. However, the closer to home the tragedy is, the more difficult it is to dismiss. 

Just before the start of this past summer quarter, my friend Bruce Arnold lost his 18 year old son Tyler in a motorcycle accident. Tyler was preparing to study air conditioning at Athens Tech and study with his dad. Bruce works in the field and takes classes in the evening. Bruce was so excited about his son going to school to study the trade he practices.

Only a parent can truly understand the feelings parents have for their children. You really cannot fathom how much you have been loved or how much of themselves your parents invest in you until you are a parent. When you are a teenager your parents unending questions about where you are going, what you are doing, and who you are going to be with are an incredible annoyance. Their interest in every detail of your mundane school day is perplexing. The reason is simple: parents have more interest in your safety and success than you do.  

Nobody celebrates your victories and accomplishments more than your parents. I have been teaching longer than most of my students have been alive, and I know that my mother is still my biggest booster. I have a 20 year old daughter and a 15 year old son, and I know I get far more excited about their accomplishments than my own. That is why I know there can be no greater pain than losing a child. Truthfully, I hope I never learn what it feels like.  

Bruce returned to school and completed his summer coursework. He explained that he felt compelled to come back to school because Tyler was so proud of his dad for going to college and so happy to be going himself. Many of Bruce’s friends counseled him to “put it behind him” and “go on with his life.” He couldn’t. Instead, he started a non-profit scholarship foundation in his son’s memory. He hired a lawyer to create the non-profit foundation, established a bank account for the foundation, started a web page to advertise his foundation, and is out personally raising money for the foundation. His goal is to raise money so other young men and women can realize their future, fulfilling their parent’s dreams. If you would like to learn more about Tyler or the scholarship foundation established in his name, go to http://www.thetylerbrucearnoldscholarshipfund.com/index.html   

Where Do YOU Belong?

You can tell a lot about someone by looking at who they hang with. The people and organizations you spend time with help form who you are and advertise to the world what you really think is important. I believe finding where you fit in is important. You may have heard people talk about networking: not a connection between machines, but a connection between people. Spending time with people that have similar interests and developing your common interests. Some of the benefits are obvious, like making valuable connections to folks that can help you. However, I believe part of the power of networking is that you find a group of people whom you enjoy being with. The truth is that most people are more inclined to put effort towards helping someone they know and like. Being with other people who share your interests makes all your activities more meaningful. Disneyworld is no fun by yourself; a big part of the magic in the magic kingdom comes from having fun with your family.

Joining an industry organization gives you immediate access to a group of people with similar interests. There are many groups organized around different aspects of the HVAC/R industry. There is a group for HVAC/R Technicians – RSES; a group for trades students – Skills USA; a group for Air Conditioning Contractors – ACCA; a group for HVAC/R Distributors – HARDI. If you teach HVAC/R you have some common interests with all of these groups. Every one supports HVAC/R education with resources and material. Trying to participate in all of these would probably not be possible for most of us, but joining and participating in one is doable for even the busiest folks. I suggest exploring what all of these groups have to offer, finding where you belong, and taking the plunge.

Each organization has an annual meeting where you can network with other HVAC/R folks, participate in training, see the latest in HVAC/R technology, and just have fun. If you have never been to a national HVAC/R convention, an opportunity coming up would be the National RSES Conference in Tucson, Arizona November 9 – 13.

Here is a partial list of HVAC/R organizations with links to their web sites where you can learn more about each one.

ACCA – Air Conditioning Contractors of America

ACTE – Association for Career and Technical Education

AHRI – Air Conditioning, Heating, and Refrigeration Institute

HARDI – Heating, Air Conditioning, and Refrigeration Distributors International

HRAI – Heating, Refrigeration, and Air Conditioning Institute

HVAC Excellence - Heating, Venitlating, and Air Conditioning Excellence

NAOHSM – National Association of Oil Heating Service Managers

PHCC – Plumbing, Heating and Cooling Council

RSES – Refrigeration Service Engineer’s Society

Skills USA

Understanding Relationships is Key

During the quiet times between quarters, our team members will often discuss what students are struggling with, what WE are struggling with, and look for ways to address these issues. The other day we were discussing why many students have such a difficult time learning how to identify the common, start, and run terminals on compressors. A few other problem areas came up – reading diagrams, superheat, subcooling, and system charge compared to superheat and subcooling. Then it struck me what all these things had in common – they are all relationships. You have to compare two or more pieces of information to arrive at a solution. Over my years of teaching, I have noticed that the more abstract a concept is, the more students struggle with it. Identifying components is usually not a problem because that is very concrete, just putting a name with something you can see and touch. Memorizing definitions is also fairly straightforward, even if it is not very exciting. Most students can give us a pretty good definition of superheat. But we lose many of them when they have to actually measure it on a unit. We lose even more when they have to use that measurement, compare it to the manufacturer’s specification, and determine if the charge is correct. I believe if you made a list of all the most important things students should learn to do before they leave you would find the most important skills involve understanding relationships. I don’t know of a sure fire way to teach relationships. I think that people who have a good mechanical aptitude readily see relationships. Students that have difficulty understanding relationships need explicit instructions and lots of practice. Teaching something that is “obvious” to you can be difficult because you have to deconstruct your thinking process so you can explain how you accomplish a task that you do innately. For example, suppose you had to teach someone how to use a screwdriver. Do you know exactly how you hold it? How do you get the screw started? What do you do after turning your wrist a quarter turn so that you can turn the screw some more? I have actually had to teach people how to use a screwdriver and it was one of the most difficult things I have ever taught because I really did not know how to explain it. Admittedly, the screwdriver example is extreme. However, the same type of deconstruction process can be used to explain more analytical processes like measuring superheat. My prescription for helping relationship challenged students is to:

Analyze the task in detail – leave nothing out and assume nothing.

Teach the students the process in explicit detail making sure they understand each step.

Practice, practice, practice!

Patience, patience, patience!

Remember, if all the students could do everything easily on their own they wouldn’t need you.

Are You Practicing for Success or Failure?

We are what we repeatedly do. Excellence, then, is not an act but a habit." – Aristotle

I would like to propose a slight revision to Aristotle’s line of thought: Success is not a condition, but a habit. Have you ever known someone that is lucky and seems to go from one success to another? It is sometimes difficult not to be envious of their success and wish we were so lucky. If the primary action you take towards becoming successful is to wish for success, chances are you will not find it. People are not successful because they are lucky; they are successful because they prepare for their success through repetitive practice. So the question is: “Are you practicing for success or failure?” You might ask “Who would practice for failure?” However, I have seen many students diligently practicing for their inevitable failure. They practice for failure by not preparing for class, arriving late, and making endlessly creative excuses for their failure to succeed. Eventually they become expert at failing – eliminating all chances of success. I will not tell you that if you work hard and put your best effort into everything you do that you will always be successful. But I can guarantee that if you do not work at being successful, you will fail. So you can take the sure thing – guaranteed failure, or you can put yourself out there and risk being successful.

The Strength Remains

Nine years ago, I was working in my office at school when a teacher from down the hall came in and said that a plane had flown into one of the World Trade Center Towers. While I was searching for information about the first plane, the second plane hit the other tower. It was only then that I realized we were under attack. I believe the trade center towers were chosen because they became an icon of American strength. Rather than weaken us, the attacks strengthened us in many ways. We proved our mettle immediately following the tragedy. Stories abound about how people rose to the challenge: from police and firemen risking their lives to politicians speaking with one voice as Americans. My favorite story involves St.Paul’s Chapel directly across the street. Somehow St. Paul's survived the shower of debris and was transformed into a round the clock hostel, providing care and support for eight months to the rescue and recovery workers. Volunteers came from all over America to work there. So many volunteers came that they had to be scheduled and their time helping was limited to allow everyone a chance to experience the blessing of helping. People cried when their time was up and they had to leave.

The towers came down. The strength remains.

Are You Giving Your Students Cognitive Indigestion?

One cold wintry Friday, the philosophy professor at a small college looked out at his class only to see a single student. The snow was deep, the wind was blowing, and the rest of the class just was not able to make the long, cold trek to school. Undaunted, the professor launched into the full text of the lecture he had prepared. He was determined to reward the student for his faithfulness and deliver his best lecture ever. He elaborated on each point. He quoted from multiple sources, contrasting their different approaches to the core argument. He gave stirring testimony about the marvelous accomplishments of visionaries who had followed the tenets of the philosophy he espoused. And finally, he concluded with a call to his audience, exhorting him to embrace the difficult but rewarding path he had just laid out. After speaking passionately for two hours straight, the professor was so excited he could not wait to ask the student his impression of the lecture. The student was quiet for a long time before he spoke. “Professor, I have to feed the cattle at my folks this afternoon. If there is only one steer in the barn, I’m not going to make him eat the whole bale of hay.”

I have sometimes been guilty of trying to feed my students the whole bale at once, trying to include every excruciating detail about a topic before they have gained a broad understanding. Information overload can cause cognitive indigestion. This occurs when the listener has a large amount of data without any real framework to organize and understand it. Most people tend to learn in stages, unfolding a little bit of the mystery at a time. The study of electricity is like this. We start with general description and then add ohm’s law to refine the idea. Then after the students have the hang of standard ohm’s law formulas, we add series and parallel calculations. After students can handle these we tell them that ohm’s law is not valid for most air conditioning work because of inductive and capacitive reactance. If you are really sadistic, you will then trot out the LCR calculations. There is method in our madness. If we were to drop all this on the students in the first week, most would become confused and frustrated. It is OK to leave out details and fill them in as the students gain subject maturity. In fact, for most folks it is preferable. It is far better to feel that you are making progress, than to feel that you are drowning in information. One of the ways that I know when a student is really “getting it” is when they comment that they are beginning to understand how much they don’t know. Typically, these are some of the brightest students – they are gaining enough insight to get a glimpse of the bigger picture. It is all right to try to teach your students everything you know. In fact, your goal should be for your students to learn more than you know. It just will not happen overnight. If you guide them well, it will happen and they will return to share their knowledge and success with you. There is nothing more rewarding.