Electrical engineering and abstraction

Before starting, I would like to recommend a book I really like for studying electronics. This book is "Foundations of Analog and Digital Electronic Circuits" by the professor Anant Agarwal and Jeffrey H. Lang. The book makes difficult concepts simple and it is full of examples and exercises to practice what one has just learn. In the case the content is not clear, one can check out the online course "Circuits and Electronics" (part 1, 2, and 3) available in edx.org. Having said that, let's jump into matter.

While science is used for understanding natural phenomena, engineering is dedicated to use it in a purposeful manner. Through scientific studies, we can abstract experimental data through analysis and simplifications, resulting in mathematical models (equations). Later, engineers can use these models to achieve specific functionalities.

As these models are subject to simplification, they may not apply in all scenarios. For example, the famous "the force equals the mass times the acceleration" (F = ma) may not work for objects moving at speeds comparable to the speed of light. So it is important to question ourselves before using mathematical models to find out if they are applicable for our purpose.

Electrical engineering is the purposeful use of the abstractions made to electromagnetic phenomena. Science describes such phenomenons using Maxwell Equations. Since these models are still very complex for most electrical engineering applications, some extra abstractions are made over them to get simpler models that describe relationships between current and voltage. This allows electrical engineers to work with algebraic equations rather than partial differential equations (phew!).

Each circuit component has its own voltage-current equation to describe its behavior in a circuit. Then, as the circuit is composed by more and more elements, it's whole mathematical description becomes complex (again!). But abstraction comes to save the day: we can apply further simplifications to describe circuit blocks or even entire circuits.

There is no limit for applying abstractions. They can be used to build systems, computers for example, that seem to be very complex if they are described in terms of the natural phenomenons that make it work. However they can be described as simple as a processing unit executing a set of instructions. Just remember the restrictions used to made these simplifications as they may lead to limitations. For example: your computer may not have been designed to work at a temperature of 200 degrees celsius!