Ah, OK. This is impossible to do if you measure the impedance at only one

frequency (since you have three unknowns -- R, L, and C -- but only two

equations, Re(Z) and Im(Z) ). What you do instead is:

1) Measure the impedance at two (or more) frequencies, set up a system of

equations and solve (use, e.g., least-squares fitting if you use more than two

equations). Most LCR meters will let you choose at least two different test

frequencies.

2) (The way people usually do this...) Use an adjustable frequency generator,

connect your circuit to its output, and sweep the frequency until you maximize

the current through the circuit (this corresponds to the minimum |Z|). The

idea here is that a current maximum is reached at resonance, at which point

f*L=1/(f*C), and now that you have enough information to solve for all the

unknowns.

3) (Seemed to be a popular lab exercise in school...) Similar to #2, you find

the 3dB points of the impedances response as well as the resonant frequency,

then you compute Q, and since you can reasure the resistance directly from Q

and R you can compute L or C from Q~=2pi*fL/R or Q~=1/(2pi*fC*R). I believe

the idea is that this approach tends to be a little more accurate than (2)

since by measuring both 3dB points you're doing a bit of averaging and are

somewhat out from resonances where, if you have a high-Q circuit, measurement

accuracy is often compromised.

If you're lucky enough to have access to a network analyzer, you just tell it

to measure S_{11} over some frequency range and it'll then find the minimum

|Z| for you and read out the R, L, and C directly at that point.

The

network analyzer approach is also useful to give you some idea of how accurate

a simple series RLC model is for your particular circuit.

---Joel