How does an RC phase shifter work?

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That link just seems to get me to the cover page of H&H's book the AoE. Did you mean to link into a page? I only have the 1st edition of AoE -- can you describe the circuit in more detail?

You get phase shifts with inductors and capacitors because of the differential equations that relate their voltage and current behavior. Quiz Question -- Can you write out those two equations for us, and tell us why you think that would be the reason for the phase shifts in RLC circuits?
 
The page # in the AOE book is 78. Just search for 'phase shifter' in the 'seach this book' window.
The neat thing about the RC phase shifter is that the phase shifts from 0 to -180 as you vary the R.