# Influence of a Capacitance Matrix of a voltage measurment

I am having a problem in understanding how, in a multiconductor system, the Capacitance Matrix influences the measure of voltage between two electrodes.

In the case that interest me we have 4 electrodes, 2 emitting ones and 2 receiving ones. We transmit a known sinusoidal current into the the emitting electrodes and we measure a voltage on the receiving ones.

We calculate the impedance of the quadrupole :

$$Z= \frac{V_{r2}-V_{r1}}{i}$$

Where $Vr$ are the electrical potentials on the receiving electrodes, and $i$ is current emmited.

It is my understanding that the measured voltage is influenced by any conductor present in the medium close-by, therefore we have to determine the Capacitance Matrix to obtain the real voltage measured.

$$V_{real} = V_{measured} \alpha C_{ij}$$

What I don't understand is the relation between the measured voltage $V_{measured}$, the capacitance matrix $C_{ij}$ and the real voltage$V_{real}$.

If any of you could help understand this I would be very grateful.

$$I = V \times C_{ij} \times i\omega$$