Two wires made of the same material have the same lengths (Physics Help)

Greetings,
need some help EXPLAINING as to why the answer is (B), the current. i am not sure. thanks so much for your assistance.

Two wires made of the same material have the same lengths but different diameters. They are connected in parallel to a battery. The quantity that is NOT the same for the wires is:
A) the end-to-end-potential difference
B) the current
C) the current density
D) the electric field
E) the electron drift velocity

The current is the only thing that is different.
The potential difference is determined by the battery that is connected equally to them both.
And the electric field is EMF / length and as both of these are the same then the field is the same for both wires.

The current density and the electron drift velocity are both a function of the electric field within the material. But as the electric field is the same for both and the material is the same then so too are these parameters.

The current is different because the voltage is the same - since they're connected to the same battery, but the diameter of the two wires are different so their resistance is different.

V = I R

or, put another way

V/R = I since V is the same and R is different I must be different.