Voltmeter in Series as self inductance of cables is significant

[egon ll]

Hello,

I am using a lock-in amplifier to measure the AC voltage across a small sample of superconducting wire located in a cryostat.
As the self-inductance and the capacitance of the wires used for the measurement are non-negligible, I have basically connected the lock-in amplifier in series with the sample.

Here is a circuit diagram:

___Constant V AC Source_______
| |
| |
| |
|_______R1_____________R2___|
| |
|_______| |_____ |
| | | |
| C1 |
L1 L2
| |
| |
|__Lock-in Amp____|


My aim is to determine the resistance R1 (resistance of the sample) as a function of AC frequency above and below the transition temperature of the sample.
The resistor R2 is supposed to make sure that the current through the circuit is constant.
It is also used to infer the current in the circuit by measuring the voltage across it (R2=47Ohms).

If V1 is the voltage across the voltage source, V2 is the voltage across R1 and V3 is the voltage measured by the lock-in amplifier,
I need to find an expression relating the 3.
The self-inductance of the wires is given by L1 and L2 and C1 is the capacitance of the wires running parallel.

V1 and V2 are related in the following way.

V2 = V1*R1/(R1+R2)

Now my question is, how do I obtain an expression relating V3 and V2?
I have tried to find a solution in a few books but I couldn't find anything.
All I could find on a Google search is that a voltmeter has to be connected in parallel which doesn't really help.

Thank you very much for your help.

 

[egon ll]

Circuit Diagram

Here is a better circuit diagram.