I saw this progression as an example on an article about secondary dominants:
C Am B7 C
Is the idea here to have B7 as the dominant of E which is the dominant of Am?
I saw this progression as an example on an article about secondary dominants:
C Am B7 C
Is the idea here to have B7 as the dominant of E which is the dominant of Am?
Is the idea here to have B7 as the dominant of E which is the dominant of Am?
Am -> B7 -> E -> Am would be a commonly used example of a secondary dominant, yes. But having C come after the B7 seems like either a mistake or just a bad example.
The fact that the B7 isn't actually followed by an E7 doesn't make the B7 any less a secondary dominant though. During the B7 you may have expected an E chord ... but, surprise? C! Then again, you could stop the song before the C, and then we could only guess if that was supposed to be the real end of it.
(You may disagree on the previous paragraph, and there are many points of view... see this question: What Constitutes a Secondary Dominant?)
If this is an introductory example to secondary dominants, then it is a bad one. It should be saved for later lessons.
You are correct to assume that B7 is secondary dominant to E. So, as piiperi said
Am B7 E Am
would be a better/simpler example.
Just to expand on the topic, I'd like to point two things out:
There are secondary dominants to other degrees of the scale (not only to the dominant). So you could have
Am C7 F Am
or even
Am A7 Dm Am
and still remain on the tonality of A minor. Also, the example you posted could be explained as secondary dominant leading to a simple deceptive cadence: C is VI of E minor. This would also work if it led to C#m (vi of E major). Then again, if you want to stay on Am, this would lead to a more distant chord. Using this example as an introductory one is a bit too much.
There are no secondary dominants in that example!
Secondary dominants are chords which lead to diatonic chirds, not actually being diatonic themselves. So, if the sequence shown is in Am, that B7 should be leading to E or Em. If the sequence is in C, the same applies.
The clue is in the name. There is only one dominant of a key - that chord built on the 5th note. Thus, in key C, it's G (or G7).
A secondary dominant is the dominant of another chord from the relevant key. Here, it's C.. Were that other chord Dm, its secondary dominant is A. Were it Em, its secondary dominant is B (or the quoted B7). Were it F, the secondary dominant is C7. Were it G, it's D(7), and Am would need E(7). Each secondary dominant includes notes which are non-diatonic - called chromatics.