What are Capacitors for?

August 17, 2005 1:29 AM

Why are Capacitors so common in electrical circuits?

I know how capacitors are made and that they can act as short term reservoirs of electrical charge. Perhaps that's the whole story but I was wondering if there's rather more to it. In particular, what they do to a currrent looks rather like differentiation (as in calculus) - does that make any sense? I'm looking for a good explaination (as in one that will bring alive all of these mysterious tubes - by metaphor or otherwise) for a highly intelligent fourteen year old who was somewhat puzzled by how many of these exotic things we needed to make a Theremin.

posted by grahamwell to technology (12 comments total)

I should add that many (but by no means all) of these capacitors are in parallel with coils, to make a resonating circuit. I stumbled with metaphors of springs and weights, I don't think I was entirely convincing and I'd much appreciate something better.
posted by grahamwell at 1:33 AM on August 17, 2005

Don't think of them as storage. The key to capacitors is knowing that as the frequency of the voltage across them increases, their resistance reduces (and the opposite way round for coils).
posted by cillit bang at 1:47 AM on August 17, 2005

Let me first just say that, like with most things in life, there's a lot more to it under the surface. Particularly, the mathematics behind a lot of the theory of electronics can get really complicated. If you train to be an electrical engineer you will read many textbooks on this subject and learn a ton of theory.

But ignoring all that, there are more or less two general things that a capacitor does:

1. Filters (or "steadies" if you wish) a signal. A capacitor can be used to take a varying signal with a wave-like form and smooth it out into a flat(ter) one. Think of the energy storage as filling up during the peak of the wave and being released during the trough, counteracting the "wave" shape of the signal. It turns out that by combining capacitors and resistors in certain ways you can even exploit this to filter out certain frequencies and let others through.

You can roughly visualize this by thinking that a small capacitor will charge and discharge quickly but will not have much storage capacity. This means that it will do well at filtering a fast-moving wave (high frequency) but if you have a lower frequency wave it will not have enough "oomph" to filter it out. Conversely a large capacitor has a lot of storage ability but it takes longer to charge and discharge, which means that it will do a good job at smoothing out low frequencies but won't have much of an effect at higher frequencies.

This all means that you can build circuits that selectively respond to certain frequencies.

2. Provides a delay. This is roughly the other side of the coin of #1. In electronics you will find that there is a lot of frequency-time dualities and this is one. Just as it is good for selectively filtering by frequency, it is also good for creating circuits where you need to measure and interval or make some delay. Think of it as pouring water in a bucket, and the size of the bucket and rate that you pour the water determines how long it takes to fill the bucket. This provides the fundamental basis of most repetitive things such as generating a pulse or a tone, or any other circuit function that requires a regular interval of time to pass (conceptually like a metronome.)

There is a LOT more to it than that, but as I said this is the fodder of whole textbooks.
posted by Rhomboid at 2:01 AM on August 17, 2005

IANAEE, but I think an important thing to consider is that most things involving electricity happen very, very quickly - electrons zipping around at the speed of light. Capacitors are one of the few components that can deliver any kind of delay or time in the circuit - they make things happen after a delay, for instance, or make things happen for a certain amount of time, or indeed deal with cyclic events. Inductors also help deliver a delay, but they're big and bulky, and can infact be replaced by capacitors.
posted by Jimbob at 4:19 AM on August 17, 2005

Rhomboid sort of has it, they're filters, but they're usually for filtering noise. Electronic circuits rely on having a stable upper and lower power supply (VDD and VSS or GND) but the operation of electronic circuits tends to introduce noise on the power supply.

Nothing in electronics is ideal, even though they're approximated that way to varying degrees. Your power rails have resistance to them and when for example a CMOS logic circuit changes from a high to a low value or vice versa the current flowing through the circuit spikes. Because the metal that carries the power supply is resistive this causes a voltage droop on the power rails. This voltage droop if severe enough can cause circuit failures. By adding capacitance between power and ground you can store energy that tends to fill in those voltage sags. The same thing happens with the ground as well.

The capacitors, known as decoupling capacitors, make up the bulk of capacitors you'll see in most circuits.
posted by substrate at 4:35 AM on August 17, 2005

To expand on the above a bit, capacitors resist changes in voltage. When the voltage across them changes (due to a current spike) they produce a current proportional to the value of the capacitance times the rate of change of the voltage that opposes the voltage change.
posted by substrate at 4:39 AM on August 17, 2005

Thanks substrate (and everyone). In saying that the current is related to the rate of change of the voltage, am I wrong in thinking that this is differentiation, ie: the result you'd get from the differential calculus or is this a red herring?

The original questioner (the fourteen year old) is showing some interest in Physics and if the answer to this simple question could highlight the uses and limits of physical metaphor whilst pointing to the underlying mathematics (in a non threatening way) that would be great.
posted by grahamwell at 4:47 AM on August 17, 2005

Capacitor: I = C *dV/dt
Inductor: V = L * dI/dt

Mathematically, capacitors and inductors are identical. Physically they are obviously very different but they are still analogous. A capacitor resists change in voltage and stores energy in the electric field. An inductor resists change in current and stores energy in the magnetic field.
posted by Rhomboid at 5:02 AM on August 17, 2005

I think it is probably best to start with the math... All electrical components are characterized by how they relate voltage to current:

v=f(i)

where f() is the electrical component.

Resistors represent a linear and constant relationship between voltage and current:

v=Ri

Capacitors and inductors represent the two possible derivatives:

i = C dv/dt and v = L di/dt

Mathematically you could imagine every other possible functional relationship as a circuit element too; people actually do this sometimes. The problem is that you have to find materials that react in an appropriate way to form a component. So in practice, new electrical components have been developed based on the physical properties of naturally occurring materials.

Why capacitors are more common than inductors, if they are, is a bit complicated. The use of capacitors on your theremin has little to do with the use of capacitors on a motherboard inside a PC.

Basically, caps probably aren't more common in the your theremin, although they might appear to be more common for some reason of convenience (two caps in parallel aren't really two caps, just one bigger cap). On a motherboard caps are more common because inductors with similar energy storage are much more expensive to make, and much larger.

I stumbled with metaphors of springs and weights, I don't think I was entirely convincing and I'd much appreciate something better.

It all comes down to energy storage. The spring weight metaphor is okay, but it is a bit funky. This page on analogous electrical and mechanical systems has trouble deciding if mass is analogous to capacitance or inductance, for example. If you introduce charge the analogy is more direct, ala the displacement charge analogy, but who knows if it is more informative... Being able to move freely between the analogies is a very good thing though, so I guess they are worth thinking about.
posted by Chuckles at 5:40 AM on August 17, 2005

I'm looking for a good explanation

For improving physical intuition I think the hydraulic analogy is much better than the mass spring analogy.

The mass spring analogy is frequently used to aid understanding of differential equations. Circuits and mass spring systems create very simple differential equations that are very similar to each other. It isn't useless from a physical intuition perspective, but it isn't ideal.

The hydraulic analogy is very good. Current flow and water flow are both particle based continuous processes, so physically they are very similar. The hydraulic analogy can also incorporate transistors and diodes. The differential equations aren't that similar though, I don't think. I'm no fluids expert, but my understanding is that it is considerably harder to solve the fluid flow equations (partial differential equations) than the circuit equations (ordinary differential equations).


Here is a pretty detailed attempt to explain capacitors and the water-capacitor. Also, NEC has a bit about tantalum capacitors that covers decoupling, which substrate mentions above.
posted by Chuckles at 11:19 AM on August 17, 2005

other posters have done a good job of answering the first question. as for whether the calculus analogy is correct, absolutely. an RC circuit in one arrangement is called a differentiator; in the other arrangement it's called an integrator, because they do approximately that: the output voltage is the derivative or the integral of the input voltage. (all of this is, of course, dependent on the circuit designer's choice of components - an RC circuit will stop integrating once it approaches a fully-charged state, f'rinstance).

on a neat tangent - lots of things can provide capacitive reactance in a circuit, too. there was an enormous device called a synchronous condenser at my old job which was basically a gigantic flywheel, wired up like an electric motor. the kinetic energy stored in the device's rotation was turned into electrical energy by the windings; this whole apparatus acted like a humongous capacitor.
posted by sergeant sandwich at 2:34 PM on August 17, 2005

The first place you typically see a capacitor is in a power supply where there is an attempt to convert AC into DC. Typically, a rectifier converts the incoming voltage which varies in a sinusoid from say + 170 to - 170 (or more often whichever voltage comes from the transformer) into a waveform where the part that would have gone negative is now positive. The voltage still varies from 170 to 0 and at about 120 cycles per second. By putting a capacitor between ground and the varying voltage these variations are smoothed out. As the voltage rises the capacitor is charged and as the voltage decreases the capacitor gives up its charge tending to stabilize the voltage. A series of two or three capacitors is typically employed. This is really just a glorified low pass filter, low frequencies (DC being the ultimate low frequency) pass through and the higher frequencies are blocked.

If a signal contains both DC and AC components and you want to remove the DC you can run it through the capacitor. Capacitors block the DC and pass the AC. This is pretty simple to imagine as a capacitor is essentially two contacts with an insulator between them called a dielectric. It allows charge differentials to build up between the conductors but prevents DC current. An AC signal riding on the DC changes the charge a bit on the conductor causing the other one to either give up or apply charge to balance things out. Thus, the variation in voltage appears on the other conductor. This of course is just a glorified high pass filter.

Essentially most uses of capacitors come down to high and low pass filters of some sort or another. A capacitor has a fixed charge at a voltage and a resistor controls how much current is applied. More current gives a faster charge. (The capacitor has resistance as well, which varies with frequency.) Controlling these parameters allows one to design a circuit which passes low or high frequencies. This is a grossly oversimplified explanation.

The Navy produced a series of publications for its technicians which really break down electronics into the basics, no college degree required:

PDF versions for purchase
Online html version

A decent Wiki on RC circuits which puts some mathematical meat behind my extremely basic explanation above.
posted by caddis at 2:51 PM on August 17, 2005