In terms of band theory, what is the difference between
a. a condcutor and an insulator
b. a conductor and a semiconductor

Explanation

a. The energy gap between the valence band and conduction band in an insulator is very large whereas in a conductors, the energy gap is very small of there is an overlapping between conduction band and valence band.
b. In a conductor, there is either very small energy gap or there is overlapping between conduction band and valence band, but in a semiconductor there is always a small gap between them.