This article describes the basics of capacitance and inductance. An understanding of calculus is helpful, but not necessary. A basic understanding of voltage and current is assumed.
A simple capacitor can be constructed out of two metal plates spaced parallel to each other. Bigger plates will make a bigger capacitor, and also spacing them closer together increases the capacitance. Real world capacitors may have a dielectric material in between the plates. This material allows the capacitor to store more energy. Large capacitors used by the power company are often filled with oil.
The current flowing through a capacitor is proportional to the rate of change of the voltage, or, mathematically, i=C dv/dt. If you don't know calculus, the dv/dt term means the rate of change of the voltage with respect to time. In plain terms, the more the voltage changes, the more current flows. If the voltage isn't changing, then no current will flow.
Practically, this means that if you attach a capacitor to a battery, at first current will flow, which will charge up the capacitor. The capacitor is storing energy, and in some ways you can think of it as a little battery, except that the energy comes from stored charge rather than from a chemical reaction. As the capacitor charges, less and less current will flow until the current flowing becomes so small you can no longer measure it. At this point the capacitor is charged, and no more current will flow.
Now, if you disconnect the battery, the capacitor is still charged, and if you connect it to something like a resistor (say, a lamp for example), the energy stored in the capacitor will discharge into the resistor. Again, the most current will flow at first, and this will slowly decay until no more current can be measured, and the capacitor will have completely discharged. For those who like the math, the charge and discharge relationships follow an exponential curve.
IMPORTANT: Quite a bit of energy can often be stored in a capacitor, especially the larger ones you find in TV sets and computers. THIS ENERGY CAN KILL YOU IF IT DISCHARGES THROUGH YOU! As always, if you don't know what you are doing, keep your hands in your pockets. Some equipment has what is called a "bleeder resistor" installed, which is a large resistance in parallel with the capacitor. Because the resistance is relatively large, the resistor does not have much of an effect on the circuit, but when the device is switched off, the resistor provides a path for the energy to discharge through (a.k.a. "bleed off"). Capacitors that do not have a bleeder resistor should be discharged using a large wattage resistor before the equipment can be safely worked on. Even capacitors that have bleeder resistors should be handled carefully, since the resistors will occasionally fail or become disconnected.
Some folks like to discharge capacitors with a screwdriver. This can be dangerous, since the screwdriver provides a direct short circuit for the current, and quite a bit of current can flow (this is the part that some folks like - you can make a nice spark or, sometimes, you can even weld the screwdriver to the capacitor terminals if the capacitor is big enough).
One interesting property of capacitors is that if it stores a charge for a long time, and then you discharge it, and then you come back to it a few hours later, it may once again have a charge on it (even though you already discharged it). This is not defying physics. A similar thing happens with heat (and in fact the equations involved are very similar). If you cool down a hot brick then let it sit, it will get warm again. More than one person has been "shocked" (quite literally) to find this property in capacitors.
Current flow in a capacitor is proportional to the rate of change of the voltage, or i=C dv/dt. Since most hobbyists don't know calculus (and probably don't want to learn it), this means that some of the more difficult circuits will not be easily solved. Fortunately, most circuits can be understood (at least from an intuitive standpoint) without a detailed mathematical solution. One thing to look at is the frequency effects of the capacitor. For this, we take advantage of the fact that any signal can be thought of as the sum of a bunch of sine waves. If the voltage function v(t) is a sine wave, or, mathematically, v(t)=sin(wt), then dv/dt = wcos(wt). The "w", which is usually a greek omega (which I can't type on a standard keyboard, but it looks kinda like a "w" so I wrote that), is 2(pi)f, where f is the frequency.
Ok, that's a lot of ugly math stuff, but note that a cosine is just a sine wave shifted by 90 degress. This means that if the voltage across a capacitor is a sine wave, the current is also a sine wave but it is shifted by 90 degrees, and it is scaled by a factor that depends on the frequency (note the omega term out in front of the cosine). At low frequencies, less current flows. At higher frequencies, more current flows. This allows us to make a really big ugly approximation, that at DC, a capacitor is an open circuit (no current flows) and at high frequencies a capacitor is a short circuit (it acts just like a conductor). In between these two extremes, the capacitor is going to VERY APPROXIMATELY act like a frequency dependant resistor. This is approximate since the capacitor is actually only storing and releasing energy. Unlike a true resistor, the voltage and frequency are not in phase, and the capacitor does not absorb any real power.
The impedence of a capacitor is given by the formula 1/jwC. Mathematicians generally use the letter 'i' in place of the 'j', but in electronics 'i' was already taken to mean current. The 'j' term is the square root of negative one (which is not a real number, but is useful in math). For any given frequency, you can determine the impedence of the capacitor and compare it to the resistances in the circuit, which may be helpful in figuring out what is going on with the circuit.
Due to its complexity, the subject of real and imaginary numbers and their application to capacitors and inductors is detailed in a seperate article.
Capacitance exists all over the place in the real world, often where you don't want it (two conductive paths on a circuit board will have a certain capacitance, for example). For low frequencies, these capacitances are small enough that you don't usually need to worry about them. At higher frequencies, they often become important. The input capacitance of a transistor is extremely important to its switching speed at high frequencies, for example.
For beginning hobbyists, most capacitors will be intentionally placed into the circuit to perform some function or another (filtering or DC blocking, for example). For these, you need to buy a capacitor from ye ol' corner electronics store (or ye ol' mail order catalog, if you prefer). Capacitors are rated in farads, but since one farad is a fairly large capacitor, they are usually rated in microfarads, which is often abbreviated with a greek mu (for micro) and an F, but since most keyboards and typewriters can't write a greek mu, you will often see it as a 'u', which looks kind of similar. 'uF' is therefore a common abbreviation for microfarad (ten to the minus sixth farads). Small capacitors may even be rated in nanofarads or picofarads. Remember than nano is ten to the minus ninth and pico is ten to the minus twelfth. Microfarads is also occasionally abbreviated as MFD.
Capacitors can be polarized or non-polarized. If it is polarized, it will have a little plus symbol on it which indicates the positive terminal. You should always keep the positive terminal at a higher voltage than the negative terminal on a polarized capacitor. If you want to have some fun (and possibly hurt yourself) then put a large reverse voltage on a polarized electrolytic capacitor. They make a nice pop (for those that aren't so swift on the uptake, THIS IS DANGEROUS! DON'T DO IT!).
The most common capacitors that a hobbyist will buy are electrolytics, which are polarized, and ceramic disk, which are not. Electrolytics will usually look like tiny round cans. Inside, they are made with two conductive plates rolled up around each other, with the dielectric material sandwiched in between them. The dielectric is the material in between the plates that allows the capacitor to store more energy.
Capacitors have two ratings. The first is the capacitance. This, of course, needs to match whatever value is required by your circuit, within the appropriate tolerances. The second rating is the maximum voltage that you can apply to the capacitor. Do not exceed this voltage. As with all maximum specs, you don't generally want to be pushing these devices up near their absolute max ratings, either. If your circuit may have up to ten volts across a particular capacitor, don't get one rated for twelve volts. Get one rated for twenty four volts. (Don't get one rated for 2000 volts, either - it probably won't work correctly in your circuit)
Electrolytics will usually have the capacitance written on it (47 uF, for example). Ceramic disk capacitors are small and cheap, but usually don't have any where near as much capacitance as an electrolytic. Your 0.1 uF capacitors that you will use to bypass the power leads on digital chips will usually be ceramic disks, for example. Also, note that the tolerance of ceramic disk capacitors is HORRIBLE. If the capacitance value is critical in your circuit, you may need to measure the value of your particular capacitor, or go to one made out of a different dielectric.
Ceramic disk capacitors are often marked with a 3 digit code, that simply tells the value in picofarads. The first two numbers will be the value, and the third will be the multiplier, similar to resistance color codes. A 0.1 uF capacitor will be marked 104 (10 times ten to the 4th power picofarads), and a 0.047 uF capacitor would be marked 473 (47 times 10 to the 3rd power picofarads).
Capacitors come in a lot of other types as well. Mica capacitors are good for RF frequencies. Mylar are good general purpose capacitors. Glass capacitors don't have a lot of the aging problems that plague other dielectric materials. Tantalum capacitors are polarized and are fairly small. Large capacitors (like those used by the power company) will often be filled with oil. RF transmitters may contain capacitors that don't have any dielectric, including air (they have a vacuum between the plates). In general, you get what you pay for. Larger capacitances, smaller size, greater accuracy, and longer life all cost more money. For hobbyist work, the cheapies will usually do fine. In fact, old capacitors out of junk equipment will often suffice for a garage built project, although you will occasionally run into bad capacitors that have failed due to their age.
An inductor can be a simple coil of wire. As with capacitors, inductance can be an unintentional part of a circuit's construction. For this tutorial, we will focus on inductance that is desired in the circuit, or is part of a component that must be accounted for. A relay coil has a fairly high inductance, for example, which means that even though it is intended only as a device to activate a switch, the inductance effect of the coil must often be taken into consideration.
Current and voltage in an inductor are related by the formula v=L di/dt, where L is the inductance of the coil, which is measured in henries (H). Similar to capacitors, inductors will usually be measured in millihenries (mH) or microhenries (uH).
Note that the above formula is fairly similar to the capacitor formula, only the voltage and current are on different sides of the equation. You will only have current flowing through a capacitor when the voltage changes. Similarly, you will only have a voltage drop across a coil when the current changes. A capacitor is going to resist changing the voltage across it. An inductor is going to resist changing the current passing through it. A capacitor will be an open circuit at low frequencies and a short circuit at high frequencies. An inductor is going to be a short circuit at low frequencies and an open circuit at high frequencies.
Inductors aren't used as much in circuits these days, since almost any circuit using an inductor can be made with a capacitor and perhaps a bit of cleverness. They still get a lot of use in higher frequency electronics, and you will occasionally still see them used as power supply chokes (filters).
The impedence of an inductor is given by the formula jwL (similar to the capacitor formula 1/jwC). Again, w is 2(pi)f, where f is the frequency, and j is the square root of negative one.
Inductors are similar to resistors for parallel and serial combinations.
Series: L = L1 + L2 + L3 + ... + Ln
Parallel: L = 1/(1/L1 + 1/L2 + ... 1/Ln)
Capacitors are similar, but opposite. Series: C = 1(1/C1 + 1/C2 + ... + 1/Cn)
Parallel: C = C1 + C2 + ... + Cn
Note that the formula for SERIES capacitors is similar to the formula for
PARALLEL resistors, and the formula for PARALLEL capacitors is similar to the
formula for SERIES resistors.