We utilized full magnetic field vector magnetogramsacquired by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) to calculate vertical electric currents in the NOAA active region (AR) 12192. The AR was tracked between October 22, 2014 and October 25, 2014 with 720 s cadence. We revealed the presence of a large-scale electric current structure – distributed electric current – with the absolute magnitude varying in the range of (40–90)·1012 A. The distributed electric current is supposed to exist throughout the entire AR, and, extending to the upper layers of the solar atmosphere in one part of the AR, it closes through the chromosphere and corona in the remaining part of the AR. To test this assumption, we have compared the temporal variation of the distributed electric current value with the flare activity level (using GOES-15 data), as well as with intensity of ultraviolet radiation (UV) in the AR (using the Atmospheric Imaging Assembly (AIA/SDO) data in channels 94 Å, 193 Å, 304 Å, and 1600 Å). We found that: i) Time intervals of enhanced flare activity are co-temporal with intervals of increased values of the distributed electric current. The absence of rapid changes in the value of the distributed electric current during solar flares can be explained by high inductance of the current-carrying magnetic loops. ii) Rough estimates of the magnetic energy carried by the distributed electric current into the corona yield the values of about 1033–1034 erg for 12192. Onlya small amount of this energy is released during flare processes in the AR. Most of this energy seems to be consumed during other dissipative processes in the corona. iii) Comparison of the temporal variations of intensity in the 193 Å UV-radiation channel with dynamics of the distributed electric current in the AR reveals a good positive correlation between these values (Pearson’s R = 0.63). The absence of a correlation between the distributed electric current value and the intensity of UV radiation in channels 1600 Å, 304 Å and 94 Å might be explained by a low efficiency of the coronal loop heating by ohmic dissipation of electric currents in the corona due to the strong dependence of plasma conductivity on temperature. iv) Our results may support the concept of equivalent LRC circuit of a current-carrying coronal magnetic loop proposed by Alfven and Carlqvist in 1967 and developed by V.V. Zaitsev, A.V. Stepanov, and others. According to this model, the large-scale electric currents must exist in the upper layers of the solar atmosphere and take part in the coronal plasma heating.