## 1 Introduction  
Since its discovery in 1911 by [PERSON] [1], the phenomenon of superconductivity has undergone an intense theoretical and experimental investigation due to its unique characteristics, such as zero electrical resistance and the complete expulsion of the magnetic field from the material when it is cooled below a certain characteristic temperature, which is known as the critical temperature. The discovery of high-T\({}_{\rm c}\) superconductors in 1986 by [PERSON] and [PERSON] [2] was a paradigm shift, revealing materials that conduct electricity without resistance at temperatures significantly higher than the previously known superconductors. This discovery has expanded our understanding of quantum physics and revolutionized the development of superconductive applications. In fact, the major part of the high-T\({}_{\rm c}\) superconductors is characterized by their ability to exhibit superconductivity at temperatures above the boiling point of liquid nitrogen [3; 4], making them more practical for real-world applications compared to their low-temperature counterparts. On the other hand, the BCS theory [5] governing the low-temperature superconductors is not applicable to the high-T\({}_{\rm c}\) ones. Despite the significant advancements, the mechanism behind high-T\({}_{\rm c}\) superconductivity remains one of the most intriguing puzzles in condensed matter physics. The cuprates family is the most well-known class of high-T\({}_{\rm c}\) superconductors, with critical temperatures reaching up to 135 K [6]. Among the cuprates, YBCO (Yttrium Barium Copper Oxide) is one of the most studied cuprate compounds and it is historically considered the first compound to become superconducting above the boiling point of liquid nitrogen (77 \({}^{\circ}\)K), at about 92 \({}^{\circ}\)K [7]. This remarkable property opened the door to potential various technological applications, such as clean energy area power applications [8; 9], Magnetic Levitation Trains (Maglev) [10; 11], the Superconducting Quantum Interference Device (SQUID) [12], Magnetic Resonance Imaging (MRI) [13; 14], and Superconducting Power Transmission Cables [15; 16]. More recently, superconductors have been essential to the development of quantum computing [17; 18]. It is worth noting that in order to use YBCO for the aforementioned applications, samples in the form of coated conductors or thin films are usually exploited [19; 20] because of their high critical temperature and high upper critical field [21; 22]. In this framework, granularity is a strong performance barrier because the intergranular current density is highly dependent on the adjacent grains' misorientation angle [23]. This implies that even with a moderate misalignment, the angles correspond to a significant reduction in the macroscopic critical current density [24; 25]. On the contrary, large-angle boundaries also form excellent Josephson junctions [24]. Moreover, it has been demonstrated that the intergranular current density controls the current transport at low fields, while at fields in the Tesla range, the critical current inside the grains (intragranular) dominates the current transport [24]. So, it is clear that the understanding of the granular structure and its impact on superconductivity is crucial for the development of practical applications that could revolutionize energy systems and electronic devices. This work deals with the AC magnetic response of an YBCO thin film by studying the imaginary component of the AC susceptibility. The choice to perform and measure the AC susceptibility derives from the fact that this technique is very sensitive to the presence of granularity in the superconductors because it can reveal the complex electromagnetic properties of the granular structure of materials [26; 27; 28; 29; 30; 31; 32; 33; 34; 35].