What is the magnitude of the current in an electrolyte? [closed]








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if a battery is connected to an electrolytic cell, **what is the magnitude of the current in the electrolyte compared to the the magnitude of the current in the wire?** This doesn't make sense to me because there are cations flowing in one direction and anions flowing in the other in electrolytes, so is the current twice the magnitude of the current in the wire? does ohm's law still hold? Is current not uniform in the circuit? I hope somebody can help. Thanks!


Edit: Sorry for asking an off-topic question. Thank you so much for the answers and comments!




By Kirchoff's Current Law ("what goes in must come out") the current flowing in total in all the branches of a circuit must be equal at all points. Hence if A amperes are flowing in the wire, as no parallel branches are present we conclude that A amperes must also be flowing in the electrolyte.


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For each 100 electrons coming to the cathode, 100 electrons are passed at the cathode to coming cations or neutral molecules. 


Similarly, for each 100 electrons leaving the anode, 100 electrons are taken by the anode from coming anions or neutral molecules. 


It is similiar within the electrolyte itself. For a given volume $\mathrm{d}V$, there is a steady state $\frac{\mathrm{d}q}{\mathrm{d}t}=0$. There are only small, initial and temporary deviations to manage the ion distribution as the reaction to the externally forced potential gradient.


If the overall current was not consistently the same across all the circuit, including the electrolyte, there would happen accumulation of the charge somewhere, leading to enormous electrostatic forces and coulombic explosion. 


For an ilustration, the charge passed in 20 s at the current 1 A is comparable to the charge of GC+ thunderstorm ligtning of voltage up to 1 GV, long up to 10 km.


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