C

In materials science and semiconductor physics, the energy gap (forbidden energy gap) between the valence band and conduction band helps to classify materials into conductors, semiconductors, and insulators.
1. **Conductors** (like metals) have a very small or non-existent energy gap, often considered as $\Delta E_g \approx 0$.
2. **Semiconductors** have a small energy gap, usually in the range of 1 eV, which allows them to conduct electricity under certain conditions (like temperature increase or doping).
3. **Insulators** have a large energy gap (greater than 4 eV), which prevents free flow of electrons at room temperature.
Therefore, we can establish the relation: $\Delta E_g^{conductor} < \Delta E_g^{semiconductor} < \Delta E_g^{insulator}$.
Thus, the correct option, which matches this relation, is the choice C: $\Delta E_g^{conductor} < \Delta E_g^{semiconductor} < \Delta E_g^{insulator}$.