How would I find the unknown resistor and capacitor values of a 2-element series RC circuit given the time constant?

Question

If I have two elements, a capacitor and resistor (both of unknown values "C" and "R") connected in series and I'm given a time constant value T for the circuit and I can choose to feed any input voltage signal into the circuit (DC or AC power through "Vin"), how do I find the values of resistor R and capacitor C? Time constant T = RC (for RC circuits). Time constant value may or may not be used in finding R and C. Voltage and current can be measured between any/all nodes (A, B, or C/ground) using lab equipment (DMM). Resistance, capacitance, and inductance may NOT be directly measured from any point using lab equipment. Please provided all your steps for both figures below (Wyzant question textbox isn't letting me insert the figures so here are the diagrams spelled out):

Figure 1: Vin-----R-------C-----ground (also connected to negative terminal of Vin)

Figure 2: Vin-----C-------R-----ground (also connected to negative terminal of Vin)

If the spelled-out diagrams above are still unclear, here is the link to the full figures: (https://app.screencast.com/BtU14TIWHXFzB).

Thank you!

Answer 1

The choice is arbritrary given your very simple premise ... only requirement is that the product RC= T