1. A method of operating an electrostatic precipitator to obtain a pure gas having a predetermined dust content with a minimum energy consumption, wherein the voltage applied is automatically controlled by semipulses, comprising: (a) recording for a given electrostatic precipitator typical current-voltage characteristics (I =f (V,ohm) for an operation with an unpulsed voltage (k =1) and different dust resistivities; (b) determining for each characteristic the lowest k value with which a pure gas having the predetermined dust content is obtained; (c) associating the thus determined lowest k value with each characteristic, and continuously automatically controlling the electrostatic: precipitator in consideration of said characteristic in such a manner that (d) the actual characteristic for the operation with an unpulsed voltage is compared with the recorded characteristics and that k value is selected which corresponds to the recorded characteristic which coincides with the actual characteristic or is next below the actual characteristic.