Which reaction would take place if we sent electric current IN a voltaic cell, electrolysing it?

I know how the voltaic cell normally works, producing current. It is not what I'm asking about. I know that normally, the Zinc electrode slowly dissolves (it is anode, $\ce{Zn -2e^- -> Zn^{2+}}$), passing electrodes to the Copper electrode at which $ H^+ $ ions from the acid electrolyte get reduced to $ H\_2 $ (it is cathode, $\ce{2H^+ +2e^- -> H\_2}$) Thereby creating electric current.


Now my question is, what if we passed current from an external voltage source to that cell?
Not in the same direction of current, like an in series battery would be connected, but in the **opposite** direction?


By doing this, I hope to block the flow of electrons from the Zinc electrode (and to get it to stop dissolving?) Then reduce some cations, like $ H^+ $ or even $ Zn^{2+} $ after I run out of $ H^+ $, which is more easily reduced?


And oxidize the anion of the acid of the electrolyte on the copper electrode?


Are any of my ideas correct?


I am sorry if this is a bad question, I am a beginner.
Please don't hate me, it's my first time posting here and I tried googling.




$\ce{Zn - Cu}$ is *not* much used these days.The common [Leclanché](https://en.wikipedia.org/wiki/Leclanch%C3%A9_cell)  $\ce{Zn - C}$ "flashlight" cell is *not* rechargeable, for the reason you give.


However, [alkaline cell](https://en.wikipedia.org/wiki/Alkaline_battery) chemistry, such as $\ce{Zn - Mn}$, has less outgassing of $\ce{H2}$ during reverse current, and there are [rechargeable $\ce{Zn - Mn}$ cells](https://en.wikipedia.org/wiki/Rechargeable_alkaline_battery). To further reduce $\ce{H2}$ production, or to recycle it back to water,


* "The cathode has a catalyst to recombine any hydrogen that forms..."
* "Zinc oxide is added to the cathode mix to,... on charge,... form oxygen."


So, at useful charging voltage, *both* recharging (i.e., plating zinc metal back) *and* evolution of hydrogen take place. However, one branch of that reaction *can* be made to be favored over the other.


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