Introduction:
Carbocations are carbon atoms with a positive charge and are highly reactive species. The stability of carbocations is crucial in determining their reactivity and the outcome of organic reactions. Two factors that influence the stability of carbocations are hyperconjugation resonance and the inductive effect. Let's discuss each of these effects in detail and determine which effect dominates the stability of carbocations.

Hyperconjugation Resonance:
Hyperconjugation refers to the delocalization of electrons in a molecule through the overlap of a sigma bond with an adjacent empty p orbital or a positively charged carbon atom. In the case of carbocations, hyperconjugation occurs when the empty p orbital of the positively charged carbon atom interacts with the adjacent sigma bond. This interaction leads to the delocalization of electron density, which stabilizes the carbocation.

Inductive Effect:
The inductive effect involves the polarization of sigma bonds due to the electronegativity difference between atoms. In the case of carbocations, electron-withdrawing groups adjacent to the positively charged carbon atom can stabilize the carbocation by withdrawing electron density through the sigma bond. On the other hand, electron-donating groups can destabilize the carbocation by donating electron density.

Domination of Stability:
Both hyperconjugation resonance and the inductive effect contribute to the stability of carbocations, but their relative importance can vary depending on the specific carbocation and substituents present. In general, hyperconjugation resonance tends to dominate the stability of carbocations over the inductive effect.

Reasons for Dominance:
1. Hyperconjugation resonance involves the delocalization of electron density, which leads to a more stable carbocation. This effect is stronger when there are adjacent atoms with available p orbitals for overlap.
2. The inductive effect, on the other hand, only involves the polarization of sigma bonds and does not directly contribute to the delocalization of electron density. Therefore, it is less effective in stabilizing carbocations compared to hyperconjugation resonance.

Examples:
1. In the case of a simple alkyl carbocation (e.g., tertiary carbocation), hyperconjugation resonance dominates the stability due to the presence of multiple adjacent alkyl groups with available p orbitals for overlap.
2. In the case of a primary carbocation, where there are no adjacent alkyl groups for hyperconjugation, the inductive effect becomes more significant in stabilizing the carbocation.

Conclusion:
While both hyperconjugation resonance and the inductive effect contribute to the stability of carbocations, hyperconjugation resonance tends to dominate due to its ability to delocalize electron density. However, it is essential to consider the specific carbocation and substituents present to determine the relative importance of these effects.