I want to use my thinkpad battery(11.1v) hooked up to a LM7805 to charge a USB Device.
What are the downsides to such a setup?
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The LM7805 is a linear dropout regulator. These are classic, robust devices that do what they do pretty well. But their intended function is to modify small voltages a little bit to maintain relatively constant supplies for things that do not use much power, like a lot of modern low voltage logic and regulation ICs. Even the supplies that do use these regulators have things in place to kind of ball-park the voltage before the 7805 rounds off the top.
All voltage dropped from one end of a 7805 to the other is blown away as waste heat across some resistance. Its not a big deal for a small voltage drop for a bias supply, but you would literally be venting about half of your input power for no reason. A fairly common chopper buck circuit or half bridge switching supply could do this with efficiencies in excess of 90%. You could even make a reasonable one out of a 555 timer, a transistor, some resistors, three capacitors and a zener diode, if you just feel like you have to play with something.
Disadvantages of 7805 in this application as already noted by others: Wasting a lot of heat, draining battery twice as fast as you might otherwise.
DC-DC converter might be a good off-the-shelf solution for you:
Hope that helps.