Ok, here's alot of information about PSU's. If you don't care to know alot of internal information then you should skip the rest of this post
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We're gonna assume wall voltage is 60Hz and 120V. Other countries do 240v and 50Hz, but the actual voltage and frequency are irrelevant for this post.
Here's some basic information:
Voltage - Quantity of potential between 2 points. Think of this as how high a cliff is you are standing on if you are gonna drop a basketball below. The higher the voltage, the higher the cliff.
Hz - # of full sine waves past a point per second.
Current - Quantity of electrons past the same point per unit of time.(usually seconds).
Ok, so now that we're all educated on some basic electrical theory let's go in depth.
120V 60Hz goes into your plug, and you need 12V DC for your computer.
First, your PSU has to take AC(Alternating Current) and rectify it. That uses a FWBR(full wave bridge rectifier). This creates a 60 hz ripple that's always the same polarity. Basically now instead of a wave that goes to a + voltage, then to 0, then to a - voltage you are always on the same side. In our case I'll say +. Now you have a rippled DC signal. The quantity of current you can rectify is based on how 'sturdy' your diodes are. Better diodes cost more, but can handle more current.
Next, you have to remove that ripple. Inductors and Capacitors are used to store a charge and then release the charge when the AC voltage is dropping to try to level out the voltage. Bigger beefier inductors and capacitors give you a more smooth voltage and less rippled voltage, but cost is a factor here. Hopefully you will have a smooth DC voltage here.
Now you have to convert that voltage to a voltage you can use. So you have to step down the voltage using a voltage regulator to control the voltage in the band you need. Again, the better the quality the components the better the chance it will operate at designed specs for the designed life of the computer, but the more expensive the PSU will cost to manufacture.
And hopefully now you have 12V of CLEAN DC power. Clean is the important part because that DC ripple can really ruin your computer. AC isn't good for DC components.
Now, there's more to this story still. Ever had feedback on your TV when you turn on your vacuum cleaner or microwave? Your PSU has to deal with that crap. Your PSU has to deal with serious peaks and valleys in voltage and current(think of your lights randomly dimming for a second or two). Basically it's like throwing rocks at a window and hoping it wont break. What is the solution? Make a window with thicker glass hoping they won't throw a rock hard enough to break it. Same scenario with your PSU. Also, your computer's loading is constantly changing. From millisecond to millisecond it's changing and your PSU has to react to the change in load fast enough to keep your voltage in specification. We might be talking nanoseconds to react, but when that's several clock cycles to computer running in the Ghz range, that makes a big difference. If your voltage regulator doesn't react fast enough then the computer operates for many clock cycles at a voltage that might be too low to accurately keep data in RAM. End result? Unstable computer. On the flip side it could operate with too high of a voltage. End result? Burn up your computer components.
Your PSU needs to be made well enough to rectify and regulate the voltage needed to maintain your computer. So as you can see, there is alot of work for a PSU to do, and there's not alot of room for error. If any part of the chain fails, it potentially destroys all the components going down the rest of the PSU, including potentially all of the components in your computer.
It's a gamble when you use a $5 power supply. Do you gamble alot? If you do, do you win regularly?