The positive charge in the nucleus is that of the protons.

A proton carries one unit of fundamental charge and is stable.

All the electrons of an atoms are outside the nucleus and revolving around it in a circular orbit because of the coulomb force.

The number of electrons in the atom is called the atomic number $Z$. Hence the total charge of electrons of atom is $(-Ze)$.

Since the atom is neutral, the charge of the nucleus is $(+ Ze)$ Hence, the number of protons in the nucleus of the atom is the atomic number $Z$.