I just wanted to tell everyone that C4 is really fun. You should unlock it as soon as you can, and I think it's equal to frag grenades. Give it a try!

does it detonate by itself after a while?

Not that I know of. There is a glitch tho, where if you have 2 (side pack mod) and throw the first and detonate, then throw the second it will switch to your weapon. You have to double tap Y to go back to the detonator, which is very annoying. If you throw both of them, then you can detonate without it going back to your weapon.