Phase Shifter: why is simple RC circuit's output 0 when phase is 90 deg?
Let's start by pointing out that circuit 1 is the same as circuit 2 and that measuring an output across the resistor will look like a high pass filter whereas measuring it across the capacitor will look like a low pass filter. The filter will have a transitional point (or 3 dB point or half power point) at: -

f = \$\dfrac{1}{2\pi RC}\$

If you measure across the resistor and the capacitor at this transitional frequency you'll see that the RMS voltage is the same at: -

\$\dfrac{V_{IN}}{\sqrt2}\$

You'll also find that |Xc| = R at this frequency and that the phase shift of the signal across the resistor is exactly 90 degrees from the voltage across the capacitor. If you messed around a bit more you will find that this is always the situation because the current through both components is the same. If current is the same then the voltage across C always lags the voltage across R by 90 degrees.

It's also true that at very high frequencies Xc is very much smaller than R so the voltage across R closely resembles the input voltage whereas the voltage across C will be very small. At very low frequencies the opposite is true - the voltage across C is very similar to the voltage on the input and the voltage across R is tiny.

Only at these extremes will the phase shift produce close to 90 degrees and that will be seen across the component that has the lowest impedance.