The class BC tells you what type of fire it is for. I looked at an automotive class BC and one that was a regular class BC extinguisher. They were the same including the dry chemical they used, only difference was the automotive one came with a mounting plate, a higher price, and was labeled differently on the out side of the box.
I could be wrong but looking at the web site below it seems that it should work for automotive use.
classification of extinguishers:
web page
EDIT: Mine must be class ABC and I thought it was only a BC, i will check after work.