## 1 Introduction
This method stands out for its efficiency and practicality compared to traditional techniques for analysing physicochemical parameters which are widely used in the investigation of fraud. According to ([PERSON], 2015), the electrical impedance technique eliminates the need for sample preparation, dilutions, use of standards, reagents, high-purity solvents, and reliance on the analyst's time and experience. In contrast, conventional methods are characterised by their complexity, slowness, and high cost. Additionally, electrical impedance offers several comparative advantages, including versatility of application ([PERSON], 2015), favourable cost effectiveness, the availability of affordable equipment, and the possibility of performing on-site analyses. The technique does not require prior sample preparation and allows for real-time results. In ([PERSON], 2015), it is demonstrated that the electrical impedance method shows high accuracy, repeatability, and recovery, with values ranging from 88.2% to 94%, which is comparable to the precision obtained with high-performance liquid chromatography (HPLC) in the analysis of ofloxacin in raw milk. The electrical properties of biological materials can be measured by employing a set of electrodes arranged and connected to an electronic circuit, which are responsible for both the injection of electrical current and the measurement of voltage, being called the measurement channel. Thus, the value of the complex impedance \(Z\), in ohms (\(\Omega\)), between the measuring electrodes, can be obtained by the ratio of the voltage between the measuring electrodes and the electrical current applied, provided that the magnitude and phase information of both is available ([PERSON], 2015). There are several studies using bioimpedance in milk, [PERSON], [PERSON], [PERSON], and [PERSON] (2018) ([PERSON], 2015) analysed pure bovine milk, finding a bioimpedance value of 89 \(\Omega\), different from milk adulterated with distilled water and hydrogen peroxide,where the bioimpedance changed to \(114\,\Omega\), and \(82\,\Omega\), respectively. [PERSON] and [PERSON] (2012) [29] evaluated the change in milk fat content through impedance spectra and conductivity measurements. The same authors indicated that such a technique could help in the development of sensors to measure milk quality, such as for the detection of mastitis. Recently, [PERSON] et al. (2019) [17] used electrical bioimpedance to evaluate the quality of fat in bovine milk, and [PERSON] and [PERSON] [30] presented the behaviour of fat and lactose with a lower amount of liquids and electrolytes, which causes a decrease in electrical conductivity, and consequently, a high value of electrical impedance. However, no reports have been found in the literature on the construction of a specific tool for food analysis, in addition to evaluating the influence of temperature on electrical impedance. In addition, there is a lack of mathematical models that consider complex food factors and matrices. Bioimpedance spectroscopy (BIS) analysis from a low-cost prototype is necessary to improve the quality control of milk, and consequently, ensure a safer product for the population consuming this food. Thus, this work aimed to measure electrical bioimpedance in samples of whole UHT milk adulterated in a laboratory with distilled water to develop a mathematical model capable of identifying and quantifying the fraudulent activity of adding water to milk.