"Now the Elves made many rings; but secretly Sauron made One Ring to rule all the others, and their power was bound up with it, to be subject wholly to it and to last only so long as it too should last. And much of the strength and will of Sauron passed into that One Ring; for the power of the Elven-rings was very great, and that which should govern them must be a thing of surpassing potency."

So, the Elven rings were bound up with the power of the One. If the power of the One should fail, the others would fail also. JRRT doesn't say explicitly how the power was bound together, but it is not difficult to imagine ways in which they could be. If the Will of Sauron was bound into the One, and JRRT tells us that the One actually governs the elven-rings, then one might deduce that Sauron had magically slaved the Rings together, using his One as the master. There must have been some sort of thaumaturgic consequence of the Master Ring being thrown into a pit of lava that would have destroyed the effectiveness of the slave rings. In this sense, the "power surge" analogy might actually strike close to the mark. I would suggest, though, that the consequence would be the opposite; a drain, perhaps.

My 2 cents
-Olorin