I am given the following block diagram of a control system (I think it also applies to electrical circuits as well with linear components. Correct me if I'm wrong). My textbook says that C(s) is connected in series with the system characterized by input v(t) and output y(t). Why is it that?
I have no explanation for the quoted text...it makes no sense.
Block diagram manipulation:
When the output of block C(s) is added AFTER the block G(s) the top path contains the product C(s)*G(s). In this case, we could say that C(s)*G(s) is in parallel (not in series) to the system characterized by Y(s)/V(s) (when C(s) would be removed from the system).
The resulting transfer function is:
Y/V=H(s)=GR/(1+GR) + GC/(1+GR)
Series connections are two blocks "in-line" the output of one gets feed to the next one, that would be R and G, or C and G in your diagram.
A parallel connection is when the same signal feeds two different blocks and their outputs get added (you might have different operations, but in the simple case you are summing them).