# Nutritional, Antioxidant, Sensory, Energetic, and Electrical Properties of Enriched Pasta
## 3 Results
### Electrical Properties of Pasta Samples  
We found out that resistance \(R\), impedance \(Z\), and resistivity \(\rho\) decrease with frequency in the range of 0.5 to 200 kHz. We used the power function as a model describing these dependencies  
\[\rho=\rho_{0}\bigg{(}\frac{f}{f_{0}}\bigg{)}^{-k} \tag{6}\]  
where \(\rho_{0}\) is the reference value of resistivity in k\(\Omega\)-m,\(f\) is frequency,\(f_{0}\) represents 1 kHz, \(k\) is the constant. In Figure 3, the frequency dependencies of resistivity for all samples are presented. All dependencies have very high coefficients of determination, ranging from 0.8384 to 0.9967; this means that the model described these dependencies very well. At lower frequencies from 20 kHz to 100 kHz, displacements between the curves exist, but above 100 kHz, the curves for pasta with carrot and elderberry are almost identical. Figure 3: Frequency dependencies of resistivity for value-added pasta samples: \(\bullet\), control; \(\blacksquare\), with nettle; \(\blacktriangle\), with carrot; \(\blacklozenge\), with elderberry. Figure 2: Mean of gross calorific value of all samples with standard error. Similar frequency dependencies were obtained for impedance (Figure 4). In particular, the control pasta and pasta with nettle powder had the higher impedance values, and the lower values were exhibited by the pasta with carrot and elderberry. In addition to regression analysis, we also modeled frequency-dependent electrical characteristics in a complex variable through a transfer function \(G(s)\) in the shape  
\[G(s)=\frac{A\,s+B}{s^{3}+C\,s^{2}+D\,s+E} \tag{7}\]  
where \(s\) is the complex variable, and \(A\), \(B\), \(C\), \(D\), and \(E\) are coefficients of transfer function. The values of these coefficients and coefficients of determination are presented in Table 6.  
The frequency at the maximum amplification of the function of the complex variable was chosen as the quantifier of specific frequency. The modeling procedure is illustrated in the flowchart (Figure 5). \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & **Pasta** & \(A\) & \(B\) & \(C\) & \(D\) & \(E\) & \(\mathbf{R^{2}}\) (\%) \\ \hline \multirow{3}{*}{\(Z\) (k\(\Omega\))} & control & \(1.075\times 10^{8}\) & \(2.43\times 10^{5}\) & 7754 & \(7.59\times 10^{5}\) & \(7.48\times 10^{7}\) & 88.50 \\  & nettle & \(9.92\times 10^{7}\) & \(2.20\times 10^{5}\) & \(1.28\times 10^{4}\) & \(7.29\times 10^{5}\) & \(5.95\times 10^{7}\) & 99.99 \\  & carrot & \(1.59\times 10^{6}\) & 3824 & 1214 & \(5.61\times 10^{4}\) & \(2.097\times 10^{5}\) & 99.99 \\  & elderberry & \(2.84\times 10^{6}\) & \(-1.34\times 10^{9}\) & 563.2 & \(5.34\times 10^{5}\) & \(7.32\times 10^{7}\) & 99.99 \\ \hline \multirow{3}{*}{\(\rho\) (k\(\Omega\)-m)} & control & \(1.051\times 10^{5}\) & \(-3.18\times 10^{4}\) & 689 & 1823 & \(1.26\times 10^{6}\) & 90.60 \\  & nettle & \(1.30\times 10^{5}\) & \(-4.72\times 10^{4}\) & \(-4.72\times 10^{4}\) & 235.7 & \(1.70\times 10^{6}\) & 94.87 \\ \cline{1-1}  & carrot & \(-6.71\times 10^{5}\) & \(-3.38\times 10^{5}\) & 179.7 & \(1.19\times 10^{5}\) & \(2.13\times 10^{7}\) & 90.45 \\ \cline{1-1}  & elderberry & \(-1.71\times 10^{5}\) & \(-3.51\times 10^{5}\) & 452.3 & \(8.26\times 10^{4}\) & \(1.16\times 10^{7}\) & 96.89 \\ \hline \end{tabular}
\end{table} 
Table 6: The coefficients of transfer function (7) and coefficient of determination for all samples. Figure 4: Frequency dependency of impedance for all samples: \(\bullet\), control; \(\blacksquare\), with nettle; \(\blacktriangle\), with carrot; \(\blacklozenge\), with elderberry. For input data sampling we used [PERSON]'s theorem, where, considering the frequency band with the value of 200 kHz, the sampling period was \(T=2.50\) ms. This time should be taken as an indicator of data propagation in the model. The sampled impedance signal for the control sample is shown in Figure 6. The frequency varied in steps up to a value of 200 kHz.