# Theoretical Description of Carbon Felt Electrical Properties Affected by Compression
## 3 Interpretation of Experimental Data  
We suggest representing the CF ability to conduct electric current by the average surface conductance (ASC) instead of the well-known use of ASR, which is the inverse of ASC. The advantages of such representation will be seen later. The values of CF ASC immersed in different liquids are placed in Appendix B. A typical graph of CF ASC in the air versus felt compression D, [%], is shown in Figure 5.  
Figure 4: Relative resistance of CF in air and immersed in ethanol solution versus relative felt volume decrease. \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline \multirow{3}{*}{Parameter} & \multicolumn{8}{c|}{h, mm} \\ \cline{2-9}  & 6.3 & 6.1 & 4.9 & 4.45 & 3.7 & 1.55 & 1.1 \\ \cline{2-9}  & \multicolumn{8}{c|}{Volume decrease, \%} \\ \cline{2-9}  & 0 & 3 & 22 & 29 & 41 & 75 & 83 \\ \hline Rdc, \(\Omega\) & 0.65 & 0.22 & 0.13 & 0.1 & 0.09 & 0.07 & 0.08 \\ \hline \multirow{3}{*}{Rac, \(\Omega\)} & 100 Hz & 0.74 & 0.17 & 0.098 & 0.092 & 0.08 & 0.059 & 0.059 \\ \cline{2-9}  & 120 Hz & 0.737 & 0.168 & 0.095 & 0.095 & 0.082 & 0.061 & 0.058 \\ \cline{2-9}  & 1 kHz & 0.737 & 0.17 & 0.101 & 0.093 & 0.086 & 0.061 & 0.057 \\ \cline{2-9}  & 10 kHz & 0.665 & 0.163 & 0.095 & 0.091 & 0.08 & 0.063 & 0.058 \\ \hline Rnt, p,u. & 1.000 & 0.252 & 0.147 & 0.133 & 0.118 & 0.089 & 0.088 \\ \hline ASC,C\({}_{\text{CC}}\), 1/(\(\Omega\)-cm\({}^{2}\)) & 0.051 & 0.152 & 0.256 & 0.333 & 0.370 & 0.476 & 0.417 \\ \hline \multirow{3}{*}{ASC\({}_{\text{AC}}\), 1/(\(\Omega\)-cm\({}^{2}\))} & 100 Hz & 0.045 & 0.196 & 0.340 & 0.362 & 0.417 & 0.565 & 0.565 \\ \cline{2-9}  & 120 Hz & 0.045 & 0.198 & 0.351 & 0.351 & 0.407 & 0.546 & 0.575 \\ \cline{2-9}  & 1 kHz & 0.045 & 0.196 & 0.330 & 0.358 & 0.388 & 0.546 & 0.585 \\ \cline{2-9}  & 10 kHz & 0.050 & 0.204 & 0.351 & 0.366 & 0.417 & 0.529 & 0.575 \\ \hline Average ASC, 1/(\(\Omega\)-cm\({}^{2}\)) & 0.0474 & 0.1893 & 0.3257 & 0.3543 & 0.3996 & 0.5326 & 0.5432 \\ \hline \end{tabular}
\end{table} 
Table 3: Resistance of dry CF. Similar graphs were obtained for CF in glycerol, alcohol, and cyclohexane. The behavior of ASC measured in \([\frac{1}{\Omega\cdot cm^{2}}]\) units can be satisfactorily described by an exponential function (3) approximating actual data with a criterion of a precision R\({}^{2}\) = 0.986:  
\[ASC=a\cdot\left(1-e^{-bD}\right)+c \tag{3}\]  
Table 4 tabulated values of coefficients a, b and c for approximating dependence of CF ASC versus compression ratio in different liquids. The precision of the theoretical approximation to experimental data is estimated by a coefficient of determination R\({}^{2}\) having a significantly high value (see Table 4). Relative dielectric constant values \(\varepsilon_{\mathrm{r}}\) for all environments in which measurements for CF ASC were made, are represented in the first column of Table 4.  
It should be noted good conformity of approximating function (3) to measured data. A tendency of coefficient a and b changings versus alteration of liquid dielectric constant can be observed. The first one is grows up with the increase of the dielectric constant whereas the second one goes down. Coefficient c has no strict propensity and variates around its average magnitude only. Notably, ASC appears to be dependent on liquid dielectric parameters. Obviously, higher electric permittivity \(\varepsilon\) positively influences CF conductivity. CF conductivity increases as a function of \(\varepsilon_{\mathrm{r}}\), which could be explained by the increase of the density on internal filaments interconnections both between themselves and with electrodes surfaces.