Resistors are inserting components.  If you put a voltage across a resistor, a current will flow through it. These three values: voltage, resistance, and current are related by an equation known as "Ohm's Law":

V=IR

where

• V is the voltage in volts
• I is the current in amps
• R is the resistance in ohms

This is a very useful equation, mostly because you can manipulate it to help you compute the difference values depending on the situation.

Let's say you are connecting an LED. You're using a 5v supply and know you need a currently limiting resistor to keep the LED from frying. An LED will have a specific and well known voltage drop across it. The manufacture's datasheet will have the specific value, but typically a red LED will have a voltage drop of around 1.8 volts. As the frequency of the emitted light increases, so does the voltage drop so a blue LED might have a voltage drop of closer to 3.3 volts. So if we have a red LED, it will have a 1.8v drop. The other 3.2v has to be across a resistor in series with the LED.  What size resistor? Starting from the assumption that you want 20 milliamps flowing through the LED (most common varieties are rated for this, but you can check the datasheet for good measure), then we use

R = V/I

That is, R = 3.2/0.020 = 160

You will want a 160 ohm resistor. More or less. In this case it's safer to use a higher valued resistor. The LED might be a bit dimmer than it could be, but if you let too much current flow through it (by using too small of a resistor) it could self-destruct.

Aside: I've generally found that 220 ohm resistor is a good value to use... so I bought 1000 of them. I've also gone with 330 ohms for red LEDs and 150 ohms for green and blue.

That brings us to voltage dividers.  If we connect multiple resistors in series and apply a voltage across them, each one will take a portion of the voltage proportional to it's share of the total resistance.

Assuming the resistances are equal, the point between the resistors will measure as half the voltage across the pair and each resistor will have half the voltage across it. If we do this with three resistors, the points between the resistors will be at 1/3 and 2/3 of the overall voltage; each resistor will have 1/3 of the total voltage across it.

This is worth noting as this is exactly what is inside the 555, as we will see later.