Resistors
What do resistors do?
In short, resistors allow current to flow in a controlled amount (determined by the voltage). You would use a resistor in series with say, and LED so that current will flow through the LED, but not enough to make it go POOF.
For those who want a more detailed answer, I will provide one.
The concept of the resistor is simple and not hard to grasp.
First of all, you probably know by now that conductors will allow current to flow through them and insulators will resist current.
A resistor is simply a mix between conductor and insulator. It is a conductor, but not as good a conductor as a pure copper wire. It is an insulator, but will allow some electrical flow through it.
Now I'll share with you the specifics.
First of all, for a resistor to be of any use, generally we must know how much current will be flowing through it.
We calculate this by a simple equation known as Ohm's Law.
Ohm's Law
Where
I=current (in Amps)
R=resistance (in Ohms)
V (or E)=voltage across the resistor,
I=V/R
This means that if you put a 3.3k resistor across the terminals of a 6V battery, you will get about .001818 amps through the resistor. Alternatively, this value is 1.818mA, or milliamps. If you didn't know that already, you should copy down the multiplier prefixes to a piece of paper and keep them near.
Now, if you recall you high school algebra class, reverseengineering equations isn't terribly hard (for me at least  but once you get the hang of it it shouldn't be a problem).
So, say that instead of current, we wanted to know how much voltage would be across the resistor if we shoved 10mA through it (prefix multipliers  10mA=.01A).
We would use this equation.
V=I*R
So, .01*3300=33V. Wow, it takes 33 volts just to shove one hundredth of an amp through a 3.3k resistor. That's bit over what you should be experimenting with if you don't already know this much, by the way. At first you should keep it at no more than 12V, where a 6V lantern battery or 9V battery should be enough.
And if we wanted to know the ohms of a resistor that was conducting 24mA with 14V across it, we would do this.
R=V/I
So that comes out to about 583 and 1/3 ohms.
So there you go. Have fun! (but not at the expense of your life  if you have complicated questions about safety or anything else really pay the forums a visit)
Notes:
Carbon resistors are slightly noisier than others (except possibly wirewound) but it is generally not a problem. It is usually not worth it to replace all the resistors in a circuit with lower noise types unless the circuit is worth paying that much for. Generally, if the circuit is a good design, proper resistors will be used to give it justice during manufacture.
Resistors will get hot if lost of current passes through them. If you've taken something apart (in which case I hope you've observed proper safety procedures and know how not to get zapped) and haven't given it time to cool down, it is unwise to touch large resistors. They are large because they have to take a large amount of power.
Types:
Carbon  Standard type. Very cheap, and good enough for most things except where lots of precision is required.
Metal Film  High quality, the best when it comes to precision and low temperature drift.
Wirewound  these will take higher current than those tiny worms you can buy at radioshack. However, since they are coils, they can be subject to interference. Thus, they might no be desirable in sensitive parts of a circuit. Their inductance can also cause stability issues when used in an negative feedback loop.
In short, resistors allow current to flow in a controlled amount (determined by the voltage). You would use a resistor in series with say, and LED so that current will flow through the LED, but not enough to make it go POOF.
For those who want a more detailed answer, I will provide one.
The concept of the resistor is simple and not hard to grasp.
First of all, you probably know by now that conductors will allow current to flow through them and insulators will resist current.
A resistor is simply a mix between conductor and insulator. It is a conductor, but not as good a conductor as a pure copper wire. It is an insulator, but will allow some electrical flow through it.
Now I'll share with you the specifics.
First of all, for a resistor to be of any use, generally we must know how much current will be flowing through it.
We calculate this by a simple equation known as Ohm's Law.
Ohm's Law
Where
I=current (in Amps)
R=resistance (in Ohms)
V (or E)=voltage across the resistor,
I=V/R
This means that if you put a 3.3k resistor across the terminals of a 6V battery, you will get about .001818 amps through the resistor. Alternatively, this value is 1.818mA, or milliamps. If you didn't know that already, you should copy down the multiplier prefixes to a piece of paper and keep them near.
Now, if you recall you high school algebra class, reverseengineering equations isn't terribly hard (for me at least  but once you get the hang of it it shouldn't be a problem).
So, say that instead of current, we wanted to know how much voltage would be across the resistor if we shoved 10mA through it (prefix multipliers  10mA=.01A).
We would use this equation.
V=I*R
So, .01*3300=33V. Wow, it takes 33 volts just to shove one hundredth of an amp through a 3.3k resistor. That's bit over what you should be experimenting with if you don't already know this much, by the way. At first you should keep it at no more than 12V, where a 6V lantern battery or 9V battery should be enough.
And if we wanted to know the ohms of a resistor that was conducting 24mA with 14V across it, we would do this.
R=V/I
So that comes out to about 583 and 1/3 ohms.
So there you go. Have fun! (but not at the expense of your life  if you have complicated questions about safety or anything else really pay the forums a visit)
Notes:
Carbon resistors are slightly noisier than others (except possibly wirewound) but it is generally not a problem. It is usually not worth it to replace all the resistors in a circuit with lower noise types unless the circuit is worth paying that much for. Generally, if the circuit is a good design, proper resistors will be used to give it justice during manufacture.
Resistors will get hot if lost of current passes through them. If you've taken something apart (in which case I hope you've observed proper safety procedures and know how not to get zapped) and haven't given it time to cool down, it is unwise to touch large resistors. They are large because they have to take a large amount of power.
Types:
Carbon  Standard type. Very cheap, and good enough for most things except where lots of precision is required.
Metal Film  High quality, the best when it comes to precision and low temperature drift.
Wirewound  these will take higher current than those tiny worms you can buy at radioshack. However, since they are coils, they can be subject to interference. Thus, they might no be desirable in sensitive parts of a circuit. Their inductance can also cause stability issues when used in an negative feedback loop.
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