# Simultaneous equations

1. Feb 12, 2006

### Just some guy

Hi,

I have the results from an experiment I carried out and basically I have a formula with 2 unknown variables in it, and 6 sets of data. Because this data is from an experiment it isn't perfect and I was wondering about the method that determines the value of the 2 constants that would best fit the data.

(to elaborate, I was plugging an AC waveform into a circuit with an inductor and measuring the current and voltage - from this I got the impedance and the frequency. Since Z^2 = R^2+X^2 where X = inductive reactance, I want to find the best fitting value of R and L with 6 sets of data for Z and the frequency of the oscillator (since X=2pifL)

Cheers,
Zachary.

2. Feb 12, 2006

### Just some guy

ok, to elaborate some more I have these sets of data:

f=496
z=5.99

f=997
z=9.10

f=1410
z=11.3

f=1900
z=13.5

f=2377
z=15.3

f=2800
z=16.8

And the formula Z^2 = R^2 + (2pifL)^2

How do I find which values of R and L which best fit this data?

3. Feb 15, 2006

### Ouabache

Do you have thoughts on how you may approach this question? If you are still stymied, just take an educated guess on the procedure. Then we can help steer you in a successful direction.

4. Feb 15, 2006

### 0rthodontist

What does pifL mean? Is that pi * f * L? If so then you could let x = f^2 and y = z^2 and do a linear regression.

Last edited: Feb 15, 2006
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