# Formula to find unknown C and Rl in RC filter

I'm not sure if it's possible to do this, it's a maths problem rather than an electronic one, but the maths is beyond me so I was wondering if anyone might know.

I can't post images on maths.stack yet but this one is suitable:

https://i.stack.imgur.com/R8uWK.png

I have a RC low pass filter, simple resistor and capacitor in series, with a load resistance R2 in parallel with the capacitor who's impedance is roughly similar to that of C at the frequencies I can test at. I can measure the voltage across R2 at more than one frequency. Can I separate the C1 and R2 impedances mathematically from this to give me a value for these 2 components? The only component I know the value of is R1.

This page http://hyperphysics.phy-astr.gsu.edu/hbase/electric/filcap2.html gives a formula for Vout in terms of Vin, so in other words the voltage across C, but it does not consider a load resistance in parallel with C. Also, of course, it's not the whole solution, I believe it's a simultaneous equation I need if it's possible at all... Maybe not possible regardless.

Can anyone help? I'm well out of my depth in the maths department here. It's a real world problem for a sensor I am working on.

## 1 Answer

Question is answered in another question subsequent to this one:

Pythagorean question for vector calculation

The 2 amplitudes across R2 I can measure are d and e, R2 is a and b is Xc at the higher frequency and 2b is Xc at the lower frequency so you can get C by plugging in the frequencies into the equation for capacitive reactance.