I am rereading an electronics book (Fundamentals of Electric Circuits; Alexander) that says that the circuits
have the total impedance
Z = R + jXc
and that the phase shift is given by
theta = arctan(Xc/R)
where Xc = -1/wC
It then says:
We should keep in mind that [these] simple RC circuits … also
act as voltage dividers. Therefore, as the phase shift θ approaches
90◦ , the output voltage Vo approaches zero.
I can see that as theta -> pi/2, Xc/R goes to infinity, meaning that C or R must be very small. In the second example, if Xc is so much larger than R, then I can see that eventually all the voltage will be across it and none at Vo. (Is that what he means by voltage divider?) However, in the first example, if C is very small then Xc is very large, and doesn't that mean that all the voltage will be across it and Vo will approach Vi? Or is C so small that it acts like a short? If the latter is the case, then why isn't C a short in the second example and all the voltage across R?