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We did a lab where we built a simple electrolytic cell. In a beaker was a solution of $\ce{CuSO4}.$ A copper strip (anode) and a copper wire (cathode) was place in it. A wire connected the copper strip to the negative DC power source and a wire connected the copper wire to the positive DC power source. The power source was turned on and the copper wire was electroplated.

Considering that both electrodes are the same material, would it be possible to create a galvanic cell by reversing the reaction?

I think it would not be possible. Since galvanic cells use spontaneous reactions to create electrical energy, you would have these two copper electrodes in a solution of $\ce{CuSO4}$ separated by a salt bridge and connected by a wire. Nothing would happen because both coppers are the same and neither one of them can attract electrons more than the other.

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The galvanic cells from the same material are possible. They are called concentration cells and they use two electrolytes of the different concentration of the same electrolyte.

But their voltage is low. In the case of $\ce{CuSO4}$

$$U = 0.0295 \log\frac{c_1}{c_2}\ \mathrm V$$


Note that the electrode naming is based on the direction of the electron flow, and their mutual polarity are switched for electrolysis versus cells (primary cells or by convention discharging mode of secondary cells ).

Anode = electrons flow upward (anabasis), an anode is the place of oxidition. (Xenophon, Anabasis, "The way upwards")

Cathode = electrons flow downwards, a cathode is the place of reduction (katabasis - the way downwards)

During electrolysis, the anode is the positive electrode and the cathode is the negative electrode.

During the cell discharging, the anode is the negative electrode and the cathode is the positive electrode.

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