[Maédhros]

Kuru has already explain to you the answer, but you might want to see JRRT own words regarding the destruction of the Ring and what would happen to Sauron afterwards.
From the Letters of JRRT 131

But to achieve this he had been obliged to let a great part of his own inherent power (a frequent and very significant motive in myth and fairy-story) pass into the One Ring. While he wore it, his power on earth was actually enhanced. But even if he did not wear it, that power existed and was in 'rapport' with himself: he was not 'diminished'. Unless some other seized it and became possessed of it. If that happened, the new possessor could (if sufficiently strong and heroic by nature) challenge Sauron, become master of all that he had learned or done since the making of the One Ring, and so overthrow him and usurp his place. This was the essential weakness he had introduced into his situation in his effort (largely unsuccessful) to enslave the Elves, and in his desire to establish a control over the minds and wills of his servants. There was another weakness: if the One Ring was actually unmade, annihilated, then its power would be dissolved, Sauron's own being would be diminished to vanishing point, and he would be reduced to a shadow, a mere memory of malicious will. But that he never contemplated nor feared. The Ring was unbreakable by any smithcraft less than his own. It was indissoluble in any fire, save the undying subterranean fire where it was made – and that was unapproachable, in Mordor. Also so great was the Ring's power of lust, that anyone who used it became mastered by it; it was beyond the strength of any will (even his own) to injure it, cast it away, or neglect it. So he thought. It was in any case on his finger.