Which graph represents the relationship between the potential difference applied to a copper wire and the resulting current in the wire at constant temperature?

since copper wire non-ohmic then the answer is 2. As the voltage across a non-ohmic conductor such as a bulb increases, the electrons carry more energy. When they collide with metal atoms in the conductor, they transfer more energy. This makes the atoms vibrate more and more. This increases the resistance and the temperature, and causes the shape of the graph seen above.