# Computing stuff tied to the physical world

## Easy Electrons – Capacitance

In Hardware on Dec 26, 2010 at 00:01

This is the third installment of the Easy Electrons series.

Let’s talk about capacitance. Or more accurately: capacitors. What are they and what are they for?

My mental image of a capacitor uses the water analogy: a capacitor is like a bucket of water:

It’s a container, and in the case of a capacitor, it holds electrical energy. How much energy depends on how much water (electrical charge) and how high up (voltage potential) it is.

If you were to take a bucket of water to the top of the Eifel tower, you’d make a pretty hefty splash on the ground when emptying it!

Thinking in terms of electricity, a capacitor is a little bit like an isolator, because, when left alone, it prevents the water from going anywhere.

Capacity is measured in terms of farads, the name was chose in honor of Michael Faraday. I’ll talk more about that in a future post.

Ok, so what is a capacitor, eh?

Capacitors are funny little beasts. When you feed them with voltage or current changes, they sort of absorb them. It’s easy to visualize with the bucket of water analogy: if you hold one end of a hose submerged into the bucket and raise/lower the other end to model voltage change, you can imagine water flowing into or out of the bucket through the hose to rapidly adapt to the position (height) of the other end.

Once the current flows, capacitors immediately adapt and start to match the input voltage. Once they do, current stops. You can’t keep a constant current flowing through a capacitor. It’s not simply a conductor.

Another way to describe this, is that capacitors only affect a circuit while the voltage changes. Once it is constant, the capacitor stops playing along and will start to look more and more like a complete isolator.

This behavior is hard to grasp. You can’t just look at one state and reason from there, you have to look at the state over time and think in terms of change. Capacitance (and induction, for that matter) is substantially more complicated as concept than resistance.

But even though it’s hard, I think I can give you a feel for why it’s so tricky, using a little analogy.

When doing calculations with capacitance, dynamic systems, changes over time, and such, you’ll quickly run into something called complex numbers, a mathematical concept with immense implications in the field of electronics and other domains of physics.

Complex numbers are… w e i r d – well perhaps not as mind-bending as quantum physics, but still: complex numbers are an extension of normal numbers, in that every value consists of a real and an imaginary part. Want an example of how weird that is? How about: you can’t take the square root of a negative number such as -1, right? Because there is no value in the world which will produce -1 when multiplied by itself. Right? Wrong. With complex numbers, there is such a value (it’s called “i”, the unit of imaginary numbers).

But not to worry. I won’t expand further on complex numbers. And luckily there’s no need!

Suppose you were looking at a child sitting on a swing, swinging happily along – image on the left:

As you watch, you can see two things going on: a sideways motion and an up-down motion. Always mesmerizing, because there is this intriguing relationship between vertical and horizontal position and things like velocity. You’re looking at the fascinating world of complex numbers, using the analogy of a pendulum.

Now imagine yourself looking at that same child swinging, but from the back, swinging away and towards you. It’s the same situation, but you’re only seeing part of the picture – image above, on the right.

What you see, is a swing moving up and down in some smooth repeating cycle. There’s much less to reason about now. You can no longer contemplate the periodic alternation of angular velocity and potential energy (i.e. height). There’s a hidden dimension which you can’t observe. IOW, you’re no longer seeing the big picture, but only half the essential information, i.e. only the real part, not the imaginary part.

That’s what makes it so hard to build up an intuition about what capacitors do. They require a richer conceptual model. Most of us are not trained to think in complex numbers, we just see quantities as a simple numerical value.

Fortunately, this need not prevent us from dealing with capacitors. We just have to work a bit more from memorized rules and water analogies, instead of innate intuition.

This is why I think of a bucket of water, and how it “dampens” all changes it is subjected to:

That’s also known as a “low-pass filter”. Very useful to turn a PWM signal into an analog voltage level, for example.

And why for me, capacitors “pass electrical changes” and then “become isolators”:

That’s a high pass filter, by the way. It doesn’t let the flat portions of the input signal through, just the edges.

Next time: a bit more about farads, charge, and really really big caps.

1. Thanks for this great explanation. It brings several chunks of knowledge I did have and glued more understanding together with your story of what is happening. Bravo!

2. There’s that synchronicity again: the water bucket analogy was used coincidently in a the gas usage post comments 2 days ago (but then in the context of heat capacitance).