Imagine you have a square-shaped plate of conductive material to which you connect 3 electrodes E1, E2, and E3 (as shown in figure below). Suppose we assume for this plate a 'pi' (aka delta) two-port network model with impedances Za, Zb, and Zc, i.e., an electrical impedance between each pair of electrodes.
I was wondering what would happen if we take an LCR meter and measure impedance between electrodes E1 and and E2 while E3 is not connected to anything. Would we measure just Za, or instead Za in parallel to (Zb and Zc) in series?
My understanding is that Zb and Zc in this model relate to currents flowing from E1 to E3 and from E2 to E3, respectively. If E3 is not connected, then no current will flow to (gets out of!) E3. So, maybe current will flow only from E1 to E2 and resistance to current flow in this path can be represented only by Za, and this is what the LCR meter will measure. I'm not sure my reasoning is sound. Any help would be appreciated.