I know, that there are some effects related to magnetohydrodynamics and can change internal resistances, but I'd like to know more about this matter
If one considers a wet battery of the old fashioned type as a kind of plasma, with free ions in a background solution, then the addition of slowly varying magnetic fields to the battery will affect the resistance to current flow inside the battery itself, and thereby any external circuit you connect it to. In this case a magnetic field parallel to the direction of normal current flow has no effect. But if you put a magnetic field across this direction it will increase the resistance according to the "magnetization", a parameter (omega*tau) which measures the ion gyrofrequency (omega) times the collision time of the ion with other ions and the solution (tau). The resistance in the direction perpendicular to the magnetic field will go something like (1 + omega*tau)^2. In the liquid state I would expect that tau is very small such that omega*tau is
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