Many projects do not actually require much knowledge about electricity. Despite what is learned in places like physics classes, it is almost never necessary to use Ohm's law to calculate voltage, resistance, and current in a circuit. Many of the components that you will use are really self-contained and just need to be hooked up properly. Really, it often boils down to reading specification sheets and documentation. The devices will say what voltage they need and how much current they will draw and all you have to do is make sure it is getting what it needs.
The MCP23017 and MCP23008 integrated circuits are a great way to add more I/O pins to a microcontroller. They use the i2c standard, so they can share the same serial line with 254 other sensors and even up to 8 other chips of the same exact type. They are particularly good for a Raspberry Pi because they have higher current capabilities than the Raspberry Pi's GPIO pins. The MCP can supply 25mA per pin and the Raspberry Pi can only do less than 16mA per pin. 20mA is enough to fully power a strong LED, so 16mA may not be enough in some cases.
These parts are designed to be used in a quadrocopter. They are sold as replacement parts to pre-built quadrocopters, but work well as interchangable parts. This is documention on the specs and how to use the parts, since none is really provided.
I have modelled these parts in Creo Parametric. However, since I am using the student edition, it would likely be uselless to anyone who wants the part for their own project since it supposedly will only work with other student licenses. Furthermore, I'm not sure the license would even allow me to do that. I am not aware of a reason why I can't show you the results of the model like diagrams and renders though.
Pulse Width Modulation (PWM) is used because a microcontroller cannot easily send a specific voltages. It really can only turn a switch on and off. To be able to send a ratio of the current voltage, something like a variable resistor would need to be digitally controlled, but we don't have that. Instead, what PWM does is essentially flip the switch really really fast. That way the average voltage can be varied by leaving the switch on for longer or shorter than it is off.
A lot of us have an old desktop computer we don't want anymore and it's good to re-use components. You'll find in each standard sized desktop, an ATX power supply. It's a standardized form factor for AC-to-DC power conversion with +3, +5, +12, and sometimes -5 and -12 VDC rails. If you look on the side, there is a sticker that will say what power it is rated to output.
Most power supplies are rated for usage in the range of 300 Watts to 600 Watts. High end ones go from 700 to 1200 Watts. That's not "toy" power. It can be dangerous and these things don't seem to have any fuses or anything in them. I melted a +5VDC wire for a few seconds when it accidentally contacted a ground. You could definitely start a fire with this and maybe hurt yourself. That being said, it is nice to have a nearly unlimited and somewhat well regulated power supply for no cost. You can get them new for about 20$ too, which seems like a good deal due to the variety of standardized voltages available.
It is not entirely straightforward to use these. They don't just turn on when they get power and there is no button for it. It is designed to be managed by an ATX compatible motherboard on computer. Basically, you need to short a specific pin to ground with a specific resistance (or use a potentiometer, like I did).