After a little research, it would appear that 自動車 is a much more formal way to refer to a car, similar to the use of automobile in English. I don't think you'd ever hear someone say it in normal day-to-day conversation though!
This app is here not just to help with conversational Japanese, but also JLPT N5, where you'll find 自動車. You'll find the kanji in Kanji Kentei level 8, which is equivalent to grade 3 of Japanese primary school (小学校). :)
I am just wondering if anyone would use the word "jidousha" in general conversation when referring to a car, instead of just using "kuruma". Or would people only use the word for talking about car companies or in news papers? Just wondering xD