Apparatus with flow-through capacitors for the purification of a liquid, which comprises: at least one cell (2) provided with at least one flow-through capacitor (4) provided with two or more electrodes facing each other, between which a liquid to be treated is susceptible to flow; electrical power supply means (13) adapted to supply a direct supply voltage (VA); a modulation circuit (14) connected in input to the electrical power supply means (13) in order to receive the supply voltage (VA) and provided with switches (22′, 22″; 23′, 23″) actuatable to apply at least one operating voltage between the facing electrodes of each capacitor (4). In addition, the present apparatus comprises a control circuit (24) which is connected to the switches (22′, 22″; 23′, 23″) of the modulation circuit (14), and is provided with a control module with pulse width modulation (PWM), which drives the switching of the switches (22′, 22″; 23′, 23″) by power supplying the facing electrodes of each capacitor (4) by means of a pulsed voltage having average value proportional to the aforesaid operating voltage.