No, because C remains natural, whereas F is raised to F#. The reason one sharp is the key of G has to do with the interval sequence of the major scale, WWHWWWH (w=whole step, h=half step). If you line up the notes of the key signature of one sharp, G is lined up as the root.
Only play what you hear. If you don’t hear anything, don’t play anything.
-Chick Corea
You should definitely read up on how to construct the Major Scale to and then perhaps on to the Circle of Fifths.
its a G because the G major scale has one #, its called the key signature whereas the C scale has no #s
Quote by KennySG
why does the key change from C to G when a sharp is added? Shouldn't it be C#?
ex:http://www.magicbooktheory.com/images/cgf_keys.jpg

The note is not added to a C. These are specific ways that understanding something called Key Signatures, are taught. If you look up Key Signatures and study those, and the circle of 5ths/4ths, you'll better understand what is going on.

Best,

Sean
The Major scale is a step pattern W W H W W W H (meaning you start on the root then to get to the second degree you go up one Whole tone to get to the third scale degree you go up another Whole. Then to get from the third to fourth scale degree you go up a Half tone etc.)

So write out your 12 notes (We will just use sharps at the moment) remembering they repeat as you go past the octave.

...C C♯ D D♯ E F F♯ G G♯ A A♯ B C C♯ D D♯ E F F♯G G♯...

The smallest step which is between any of the two notes that are next to each other is a half tone or semitone. Two half tones is equal to a whole tone. So from C to C♯ is a half tone and from B to C is a half tone. But from C to D is a whole tone and from B to C♯ is a whole tone.

Now simply start on C as your first scale degree then move up and circle each note you get to when applying the following step pattern
Whole Tone - Whole Tone - Half Tone - Whole Tone - Whole Tone - Whole Tone - Half Tone.

You should end up with this: (Just pretend the bold notes are circled)
C C♯ D D♯ E F F♯ G G♯ A A♯ B C

And that is the major scale starting on C - or the C Major Scale. :p

Now write the 12 notes out again and do the same thing but this time use G as your starting point using of course the same step pattern (It is that particular step pattern that makes it the major scale) Let us know what you come up with.

Once you've done that we can go into a little more depth outlining the relationship between the two keys and then once you've got that we can introduce you to the circle of fifths. It's not too tough but you just need to go one step at a time.
Si
Last edited by 20Tigers at May 20, 2010,
Just buy a book on beginning music theory and you should get it pretty quick honestly, its not that hard to understand. Hell, just google circle of fifths, Im sure you'll find something that'll work.