You know what we really need in the playground? We need to gather all of these little tidbits of information (ie, calculations of base resistors and why, calcs for LED current resistors and why, etc) - in one spot.
For myself, I have been trying to come up with a list of these items, following things from these forums, and things online (I found this resource, which seems pretty good, actually - but there are others):
http://www.kpsec.freeuk.com/ - "The Electronics Club"
Its been almost 2 decades since I really calculated out these values (back when I went to a local "tech voc school" here in Phoenix); since then when I built things I essentially have done the "guess and pray" method, and if things got hot, changed the values up, if things didn't work, drop 'em down. That's not a good method, and I know this, but I hate doing math. With that said, for the project I am working on I want things to be more solid. This has led to me seeing these calcs everywhere, and I understand ohm's law and such, but it has been a while since I looked at this stuff...
So - refresher course time for me - no problem here, and it is coming back to my old-fart brain. But for others, newbies to electronics, it would be great to have something local to arduino.cc that we can point to (ie, on the playground, or somewhere) and say "see - this is what you need to do".
This resource should encompass things like LEDs and transistors, what and how to use resistors, capacitors, diodes, coils, etc - everything - in the proper way, with the proper math to calculate values and how, and why - plus rules of thumb.
Other things I have found helpful (which may already exist somewhere on the playground, I haven't looked) would be resistor color codes (or a calculator - I love the one on my google phone, beats having to remember the "bad boys ..." mneumonic) as well as a capacitor value conversion chart (plus perhaps an inductor chart); I have found ones online that have been immensely helpful, but it is another area that I need to refresh my old head on. I guess I have been involved in software waaaay too long; oh well.
These things just seem scattered; I have found the site I referenced earlier to be very helpful, although it is UK/euro-centric (in a way, this is nice, because they use a slightly different - actually I think it is SI - method of representing certain values and such for resistors/inductors/capacitors - and it has helped me to get my head around those notations). Rather than referencing that site, though, I would prefer something local to arduino.cc (or at least maybe a local copy of the site with permission of the author?).