The key behind changing dominant chords and unaltered dominant chords is called Tension and Release. A dominant 7th chord has a natural quantity of tension built in to it. You can hear it is not settled, it wants to go and move someplace. By contrast, the Major chord IS a settled chord, it's a feeling of rest.
The solution is the 3rd and 7th notes. Listen in the case how the 3rd and 7th are extremely dissonant. This period is called a Tri-tone. If you look at a piano and pick two notes, then state C and C one octave higher, and find the note that's directly between the two notes, this is the tri-tone. In this case it's F#. Looking at the circle of 5ths graph, you can see also that the tri-tone is the note directly across from the one you are looking at. See that F# is straight across from C. The word tri-tone literally means three tones. Go up three complete steps from some note, and you will be in the tri-tone. Some others call it an Augmented (eloquent ) 4th, or Diminished (flat) 5th. The sound of this tri-tone wants to obviously collapse. The 3rd note wishes to come up 1/2 step, and the 7th note wants to go down 1/2 step. This starts out as anxiety, and then releases the strain.
The new notes that they form are C and E. Collectively E and C are the root and 3rd of the significant chord of our E. V7 I! This is the reason why the ii V7 I connection is so powerful! V7 wants to become I chord due to the tension and release. The whole notion of using altered dominants is to create MORE strain on the V7 chord, so that the release is even more satisfactory!
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