Passive Components

Passive components are components that don't actively change the signal applied to them, and include things like resistors, capacitors, transformers and inductors.

Resistors

Resistors introduce a measured amount of resistance into a circuit. The standard unit of measurement for resistance is the ohm (Ω). One thousand ohms is one kilo ohm or 1kΩ, while one million ohms is one megohm or 1MΩ and don't normally have voltage ratings. Resistors are commonly available from 1Ω all the way up to several million ohms, and with power dissipation ratings from ¼ watt up to about 25 watts. For a given power rating, a resistor of any value will be the same size. Larger power ratings mean physically larger resistors. The most common resistors are ¼W, and when reading a schematic these are assumed to be the "default" resistors, where a higher powered resistor is called for it will generally be noted.

The most common use of resistors is to control the amount of current flowing around a circuit. Higher resistance means less current for a given voltage. Higher voltages mean more current for a given resistance. Resistors affect AC and DC the same way. The formula for determining how much current a resistor passes at a given voltage is voltage / resistance = current in amps. Current traveling through a resistor naturally generates heat, and the more current, the higher the heat (the heating elements in appliances are resistors which pass a large amount of current). Resistors have heat ratings specifying in watts how much heat the resistor can safely handle. Since I've already showed you how to derive wattage from current and voltage, this will let you easily calculate the power dissipated by a resistor. Let's say we want to connect a 10kΩ resistor across a 12V power supply,  12V/10,000Ω=0.001A, 0.001A×12V=0.01W, which means we could safely use a ¼W resistor.

Another common use of resistors is as a potential divider. Let's say we have two resistors that for the sake of argument we'll say are 10kΩ. If you place these resistors across a 12V power supply, the voltage across both resistors will be 12V, but the voltage across each resistor will be 6V. Since the amount of current that can be pushed through a voltage divider is limited to the amount of current that will flow through the largest resistor, it wouldn't be of much use for something like dropping line voltage in a power supply. This type of potential divider is mainly useful for small signals, powering small, low-current things like LEDs, and providing reference voltages for other components.

A potential divider that you're probably already familiar with is the volume control on your stereo. This type of voltage divider, called a potentiometer,  is a fixed resistor with a sliding contact. The audio signal is connected at one end, the ground connected to the other, and the output is connected to the sliding contact. This allows you to vary the voltage at the output from 0V all the way up to the input voltage.

There are four common types of resistors, specified by the type of material providing the resistance. Small resistors under ½W are generally carbon film or metal film. These type of resistors are made by vacuum depositing the resistive material onto a ceramic form, then coating the whole thing in epoxy, tan or brown for carbon film and green or blue for metal film. Carbon and metal resistors are generally interchangeable, although metal film resistors tend to be more precise. Slightly larger resistors up to about 5W are made from metal oxides, and look similar to their smaller cousins, but with a matte rather than glossy finish and are generally color-coded a bluish-green. Metal film, carbon film, and metal oxide resistors use color coded stripes to indicate their value, where each color stands for a number.

The largest resistors with dissipation ratings 5W and above are usually wirewound resistors, which are made by wrapping a resistive NiCr wire around a ceramic former the sealing the whole thing in a ceramic block. These resistors can be quite large, a 10W wirewound resistor is almost 3" long. This type of resistor is usually used in high power applications like speaker crossovers and power supplies. Its value and wattage are usually printed on the body of the resistor.

Capacitors

A capacitor consists of two conductors separated by a layer of insulation called the dielectric. A capacitor can store a DC charge in the electrostatic field between the conductors. It's ability to store a charge is call its capacitance, which is measured in farads, abbreviated F. Since the farad is a ridiculously huge value, you're more likely to run into components with capactitances specified in microfarads (μF) which are 1/1,000,000 of a farad and picofarads (pF) which are 1/1,000,000,000,000 of a farad.

The capacitance of a capacitor depends on three things, the size of the conductors, the thickness of the dielectric, and the dielectric constant. Thinner dielectric and larger conductors mean higher capacitance values. Higher voltage ratings mean thicker dielectric. Because of this, capacitors tend to grow larger as the capacitance and voltage rating increase.

Capacitors are commonly available in a range of sizes, depending on the type of capacitor. In addition to the capacitance, a capacitor will also have a voltage rating, either specified as V, WV, or WVDC (working volts, DC). It's important not to charge a capacitor past its voltage rating. Taking a capacitor past its specified maximum voltage can cause the dielectric to fail, causing a DC short and catastrophic failure of the component and anything it's connected to.

Unlike a battery, a capacitor can be charged and discharged instantly, as long as there is enough current available. A capacitor's ability to store a DC charge is useful for things like rectifiers, where the choppy output of a diode is "smoothed" by the reservoir capacitor, which fills up while the diode is conducting, and releases its charge when there's no more power to charge it.

Like transformers, capacitors are capable of passing an AC voltage while blocking DC completely. You'll see this often on amplifiers, where a large output capacitor is used to block the DC power supply voltage while passing the AC audio signal. This also makes them handy for "coupling" two or more circuits with different DC potentials while still allowing an AC signal through.

Capacitance is a form of reactance. For now, you can think of reactance as resistance that only affects AC. This means that you can design filters using capacitors that pass only certain frequencies, shunt AC voltages to ground, or construct voltage dividers for AC in the same way you would use resistors in a DC circuit. Larger capacitance values mean less resistance to AC, and more current flow. The frequency filters found in speaker crossovers, such as Butterworth, Linkwitz-Riley, and Chebyshev filters usually contain at least one capacitor.

Aluminum Electrolytic

Aluminum electrolytic capacitors are composed of an aluminum can, a spiral of thin aluminum foil, and a spiral of paper wetted with a conductive electrolyte of some sort. The foil forms one conductor, and the can and electrolyte form the other. The dielectric is a thin layer of non-conductive aluminum oxide on the surface of the foil. Since the dielectric is so very thin (a few micrometers), electrolytic capacitors have the largest capacitance values commonly available. They're used any time a large (over 1μF) capacitance is called for, and are commonly used as reservoirs in power supplies, coupling capacitors where a large current is called for and in filters where other types of capacitors aren't practical. Common values are from 1μF to 10,000μF, although specialty capacitors are available with as much as 1F of capacitance. Voltage ratings for electrolytics can range from 16V to hundreds of volts. Power supply filters are usually 470μF and up, with higher values being necessary for supplying larger loads.
All capacitors have a value referred to as equivalent series resistance or ESR. In an ideal capacitor, the ESR would be equal to zero, while in most real-world capacitors the ESR will be somewhere under 1Ω. Electrolytics have the highest ESR of any type of capacitor, which can equal several ohms and drifts upward as the capacitor ages, which can cause problems in some critical circuits. Electrolytics are generally the least reliable type of capacitor, since their capacitance relies on the electrolyte staying moist. Electrolytics will generally dry out after a period of years, especially if they're not being used. You can lessen the chance of this happening by buying good quality capacitors. Designers generally tend to try to find a way around using electrolytics in critical applications or in applications with changing pressure, mechanical vibration, or extreme heat.
Unlike other types of capacitors, electrolytics are (usually) polar, having a positive end and a negative end. Because of this, they get their own schematic symbol, which usually has a series of diagonal lines in between the plates. Electrolytic capacitors will always have their positive end marked on a schematic with a plus sign. The capacitors themselves usually have some highly visible marking, like a series of minus signs, pointing to the negative lead, which is also physically shorter. Installing an electrolytic capacitor backwards literally causes it to explode. The grooves incised on the top of an electrolytic capacitor are there in case the capacitor does become reverse biased, so that it will explode with minimal damage (hopefully) to the surrounding circuitry. Non-polar electrolytics are available, and are used in speaker crossovers and other applications requiring them to pass an AC signal with negative and positive components.

Film

Film capacitors are very commonly used in audio and other circuits, primarily as part of RC filters, and as coupling capacitors. They are commonly available in a range of values from a few pF up to several μF and in voltage ratings from 50V all the way up to several thousand volts. Traditionally, they are used for values over 0.001μF up to 1μF, where ceramics are used for lower values and electrolytics are used for larger values. Higher quality speaker crossovers use high value film capacitors in place of non-polar electrolytics. There are a few different types of film capacitors available. The most common are metallized polyester, which are made by vacuum depositing a thin layer of aluminum onto a polyester film, then winding it up and dipping it in epoxy. Another common type is polypropylene film, which uses layers of thin foil with a layer of polypropylene sandwiched in between, once again, the whole thing is wound up and dipped in epoxy. The result is an extremely reliable capacitor that is resistant to water, heat, shock and other stresses and should perform reliably for the life of the device as long as the voltage ratings aren't exceeded. Excess voltage can cause arcing, which permanently damages the dielectric, resulting in a "leaky" capacitor that must be replaced. Film capacitors are commonly available in tubular form with axial leads and "orange drop" types with radial leads.

Ceramic

Ceramic capacitors are perhaps the most reliable type of capacitor. These are used extensively in commercial electronics, and are the most common type of capacitor found on PCBs as surface mount components. Like film capacitors, ceramic capacitors are commonly used as coupling capacitors, and for RC filters. They consist of layers of aluminum sandwiched between layers of a ceramic material, which is fired in an oven to harden. This type of capacitor is extremely resistant to heat and water, but is less resistant to shock than a film type capacitor. There are two types of ceramic capacitors commonly available. The older ceramic disc style are usually orange or brown and about the same size and shape as a lentil. They're inexpensive and generally reliable, but aren't usually suitable for frequency critical circuits, since their value may drift with changing temperatures. The newer multi layer ceramic (MLCC) capacitors are more stable, and can used in frequency critical circuits. They can be distinguished  from ceramic disc capacitors by their shiny epoxy coating. They are available with a range of dielectrics, usually denoted by a letter and a number. Type C0G dielectrics are the most frequency stable and are used for applications where precision timing is important, such as PLLs. Common values for ceramic capacitors are from a few pF up to a few μF, with the most common values being in the tens to thousands of pF range. Traditionally, ceramic disc capacitors are used for values under 0.001μF, and multi layer ceramics are usually used for up to 0.1μF, with larger values being in the range of film capacitors. Voltage ratings can range from 50V up to tens of thousands of volts.

Inductors

Like capacitors, inductors are a form of reactance, which presents a resistance to AC voltage. They generally consist of a coil of wire, wound around a nonconductive former or a magnetic core material like iron or ferrite. Inductance is measured in henries, abbreviated H, with larger values generally meaning more turns of wire or larger loops and physically larger inductors. Adding a magnetic core increases the value of an inductor. Unlike capacitors, inductors generally don't offer any resistance to DC. This property makes larger inductors called chokes useful as filters in power supplies. The choke is installed in series with the DC voltage source and the component being powered, the current flowing through the choke creates a magnetic field in the core of the choke (which, like a transformer, is often made from iron laminations), when the current flow stops or slows down, the collapsing magnetic field resists the change, kind of like an electrical version of a flywheel, which smoothes out any variance in the power supply.

Smaller inductors are used frequently in "tuned" or resonant circuits, and show up a lot in radio frequency circuits, as well as filters where certain frequencies need to be passed and others blocked. The type of filters used in speaker crossovers, like Butterworth, Linkwitz-Riley, and Chebyshev filters usually contain at least one large value inductor.

Inductors are available as discrete components, resembling fat, green resistors, although you don't see these often. Speaker crossover inductors are usually 18 gauge or larger copper wire wrapped around an iron core or plastic former. In consumer electronics, where a frequency filter is called for it's usually more economical to use capacitors instead of inductors.

In RF circuits the coils are generally custom wound and have very small values with air cores. If you need to wind your own inductor, many calculators are available online to show you how many turns of wire you'll need.

Transformers

A transformer is composed of two coils wound around a common core, usually made of iron laminations. Transformers are most commonly used in power supplies, where they convert high voltage, low current AC voltage to low voltage, high current AC or vice versa, while completely blocking DC. The input of the transformer is called the primary, and the output is called the secondary. The voltage difference between the input and output is dependent on the ratio of turns between the primary and secondary. For example, a transformer with a 120V primary and a 10:1 winding ratio will output 12V from its secondary. Transformers with a 1:1 ratio are referred to as isolation transformers.

A transformer's secondary is electrically isolated from its primary, so measuring the voltage between one leg of the secondary and either leg of the primary or to ground will give a value of 0V. Neither one of the secondary's outputs is a true ground, since they're both constantly varying. The voltage comes from the two waves being out of phase with each other. The secondary only presents a voltage relative to itself. This is why it's safer to work on a live circuit powered by a transformer than one connected directly to mains power, which is 120V RMS from the ground. Autotransformers, which are also called variacs, are a type of variable voltage transformer that does not provide any isolation.

Some transformers provide multiple taps. A transformer with a center tapped secondary is able to provide one voltage when connected to the outer leads of the secondary, and half that voltage when connected to one of the outer leads and the center tap. A transformer with a center tap is specified like this: 12-0-12, which indicates a 24V transformer with a 12V center tap, or 6-0-6 for a 12V transformer with a 6V center tap. An everyday example of a center tapped transformer are the large transformers bolted to utility poles. These transformers provide 240V, with a center tap. The center tap is used as a ground, and may actually be connected to the ground, and one of the end taps is used for 120V appliances, while appliances like ranges and dryers use the 240V provided by the end taps only.

Another use for transformers is to match the impedance (think of it as electrical springiness) of two circuits. An example of impedance matching transformers are the output transformers in audio gear, which match the high output impedance (up to around 10kΩ) of a tube amp to the low input impedance (around 8Ω) of a loudspeaker. Another example are the line matching transformers that come with VHF/UHF antennas that convert the 300Ω balanced output of the antenna to the 75Ω single-ended signal required by a coaxial cable.

Crystals and Resonators

Crystals and ceramic resonators are used to provide an oscillating frequency. The most common type of crystal is a quartz crystal enclosed in a metal can. When a voltage is applied, the crystal oscillates at its specified frequency. This type of oscillator is extremely accurate, and can be used for timing things. The most common uses of quartz crystals are for clock signals for computer processors and data circuits and as references in timekeeping devices. They're also used in RF circuits. Crystals are available with a wide range of operating frequencies, from a few kilohertz (kHz) up to several gigahertz (GHz) with the most common ones being from 0.5-20MHz.