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An electrolyte contains positive and negative ions. The molecules that constitute the ions will split in solution to the ions through electrolytic dissociation, irrespective whether an electric field is applied.
When the electrodes of a voltameter are connected to a battery, a Potential difference is set up, such that the positive ions move towards the cathode and negative ions drift towards the anode.
The directional movement of ions is the electric current flowing through the electrolyte. The electrolytic solution can conduct electricity due to the fact that electrolytes in the solution can conduct dissociates into ions
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