How Do You Build an RLC Circuit with Specific Phase and Amplitude Requirements?

[girrafeblue22]

I have been given the task of building an RLC circuit that is driven at 10kHz, has an output amplitude of 1/sqrt(2) and is 45 degrees out of phase from the input voltage.

I am not really even sure where to get started.

Any tips will be greatly appreciated.

 

[technician]

The first point I would note is that 45 degrees out of phase means that the value of
(Xl - Xc) or (Xc - Xl) must equal the value of R.
This means that at your chosen frequency (10kHz) Xl must = 2 x Xc This would be 45 leading
OR Xc must = 2 x Xl this would be 45 lagging
This means that the supply voltage Vs = Vr x √2 (or Vs = Vl x √2,,,, or Vs = Vc x √2 )
Hope this helps
PS when I say leading or lagging I mean supply volts with reference to the current (or Vr)