Monthly Archives: August 2012

The Language of Math

Thus far I have avoided bringing math into my posts about the physical phenomena that underpin modern electronics. Math is one language we can use to discuss physics, and it’s certainly a language that lends elegance and precision. I have an undergraduate degree in math, and partly chose physics because it seemed to me to be the most math-heavy of the sciences, so certainly I see the appeal! However, I think that verbal descriptions are very valuable as well, both for people with a strong math background and for people who’d rather avoid it. The best undergraduate textbooks I used had a combination of verbal and math explanations (for example, the excellent Electromagnetism and Quantum Mechanics textbooks by David Griffiths).

So in general, I think that if you want a really thorough understanding of science, you have to dig into some math. You also have to dig into some physics, and you have to dig into some chemistry, and you have to dig into some biology. You even have to dig into quantum mechanics, which is not as bad as many people think. It’s all interconnected, and the many different languages of science play off each other in interesting and unexpected ways. But if you can only explain something in math, and not using words, then your understanding is incomplete in my view. And for those with an interest in science who don’t need to dig in to all the details, the verbal explanation is usually the best place to start!

On top of which, there are so many ways to explain a concept verbally (or using video or other media, as Erin recently posted). The simplicity of math-based explanations is wonderful, but can feel like a dead end if the math doesn’t click mentally. But if you are open to a diverse range of explanations, it’s possible to try many different approaches until one finally puts all the others into perspective. I have found this to be the best way to get my own head around really bizarre scientific ideas, to approach them from many sides until they finally make sense.

That said, sometimes the mathematical interpretation of an idea leads somewhere new, and thinking about math becomes necessary to understanding the new idea! I plan to keep approaching these topics from the verbal side, and we’ll see how it goes with the subject of the next post!

Active and Passive Circuit Components

Now that we have several different circuit components under our belts, it’s helpful to try to classify the behavior that we’ve seen so far. Resistors, capacitors, and inductors respond in a reliable way to any applied voltage that induces an electric field. Resistors dissipate heat, capacitors store charge, and inductors store magnetic flux.  These responses always occur and cannot be manipulated without manipulating the very structure of the material which causes the response. They don’t add energy or electrons to a circuit, but merely redirect the electrons provided by an external source. Thus these are called “passive circuit components”.

Transistors also have a predictable response to a given voltage, but that response can be changed by tuning the gate voltage in order to open or close the conducting channel. Effectively, the transistor can be in one of two states:

  1. Functioning like a wire with a small resistance, passing most current through while dissipating a small amount of heat.
  2. Functioning like an insulator with a high resistance, blocking most current and dissipating more heat.

The controlling gate which allows us to pick between these two states can actually add energy to the system, increasing the current output, thus the transistor is called an “active circuit component”. Circuits that do calculations or perform operations are usually a combination of active and passive circuit components, where the active components add energy and act as controls, whereas the passive components process the current in a predetermined way. There are other system analogues to this, such as hydrodynamic machines. Instead of controlling the flow of electrons, we can control the flow of water to provide energy, remove waste products, and even perform calculations. An active component would be a place where water was added or accelerated, whereas a passive component might be a wheel turned by the water or a gate that redirects the water. But in electronics, with electrons as the medium, active components add energy and passive components modify existing signals.


Why Science Communicators are Important

Why Science Communicators are Important

A little Friday fun.