ok this is probably a really easy question which only might need a one word answer, buuuut...

if you are playing a song in the key of C without a capo, and then you put a capo on the second fret and play it, is it not in the key of D?

eg. first fret makes song in C now in C#/Db, third D#/Eb, etc etc

thanks a lot in advance for your help guys