Ohm's Law.


150 watts / 13.8 volts = 10.8 amps.


The cigarette lighter will be just fine.

That tiny inverter will crap out after a few days of hard use.

Go 250 at least, preferably 350.

 

Don Rowe is goto Man for power inverters and a 350 watt pure sine wave inverter is $103,. Computers don't enjoy running on dirty power and the Tripplite is a modified square wave, if your power inverter can't light up a fluorescent tube then you shouldn't use it on a computer or a tv or a xbox, etc.
http://www.donrowe.com/Samlex-SSW-35...sw-350-12a.htm, 3 amp continuous draw.

$150 will buy 600 watts of clean power and 5.2 amps continuous current draw, i just might buy this one for myself.
http://www.donrowe.com/Power-Bright-.../aps600-12.htm

 

I wonder how confused the OP is by now...

 

Good stuff!

 

Hope not as much as me about now! Thanks to everyone for the questions and the information.
Must study more... Can't learn it all at once. But I try!