The potential to which a conductor is raised depends on both the amount of charge and the geometry and size of the conductor.

Amount of Charge:
The potential of a conductor is directly proportional to the amount of charge it carries. This is known as Coulomb's Law, which states that the electric potential is directly proportional to the charge on the conductor. In simple terms, the more charge a conductor has, the higher its potential will be. This can be explained by the equation V = kQ/r, where V is the potential, Q is the charge, r is the distance from the charge, and k is the proportionality constant.

Geometry and Size of the Conductor:
The geometry and size of the conductor also play a crucial role in determining its potential. The potential at any point on the surface of a conductor is the same. This means that the shape and size of the conductor determine the distribution of charge on its surface. For example, a conductor with a larger surface area will have a lower charge density and a lower potential compared to a conductor with a smaller surface area and higher charge density.

The shape of the conductor also affects its potential. For example, a spherical conductor will have a uniform potential throughout its surface, while a cylindrical conductor will have a non-uniform potential. This is because the electric field lines are perpendicular to the surface of a conductor, and the shape of the conductor determines the distribution of these field lines.

In addition to the shape and size, the presence of other conductors or charges in the vicinity can also affect the potential of a conductor. The potential of a conductor can be influenced by the charges or potentials of nearby objects through the process of induction or by the presence of a charged object in its vicinity.

In conclusion, the potential to which a conductor is raised depends on both the amount of charge it carries and the geometry and size of the conductor. The amount of charge directly determines the potential, while the shape and size of the conductor determine the distribution of charge and the potential at different points on its surface.