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[Harry Potter] How exactly are some wizards more powerful than others?

In Harry Potter, both Dumbledore and Voldemort are described as being extremely powerful wizards. My question is: how exactly are they more powerful than a regular wizard? Do they simply know more spells? How does a wizard know how powerful he is? Can a wizard become more powerful with time? Seeing as lots of spells seem to have uniform effects regardless of who is casting them, it seems that knowing more spells, rather than any kind of intrinsic power, would be more useful.

Also, a related question, the Elder Wand is described as being the most powerful wand in existence. How exactly is it more powerful than any other wand?
gpt
I believe in HP, at least the books, "Power" Is a combination of two things. Reserves, and Knowledge.

Magic in the Potterverse. Every wizard (probably) has a reserve of magic. Different spells take different amounts of magic. Think of it like Chakra in Naruto. You CAN run out.

Knowledge is just that. Spells you can cast and know how. Dumbledore, having given his life towards The Greater Good, has dedicated his life to magical studies, ever since he was a child. Since he's quite old, he knows a lot. He also has a large amount of magic.

Voldemort, succumbed to the darkest of arts. Dark arts are always more powerful, but they have a cost. Riddle's cost was eventually his humanity.

To prove that it is Knowledge & Power, think to The Golden Trio. Hermione isn't very intristically powerful, but more than makes up for it with her studies. Ron, on the other hand is the opposite. He comes from a very powerful and old wizarding family, but doesn't study worth crap. He relies on his own power to match with Hermione. Harry is just about the balance, except he is more powerful than Ron. He doesn't study as much as Hermione, but more than Ron. This explains how HP is considered the more powerful of the Golden Trio. He has a considerable amount of power, and some knowledge to back it up.

I think that The Elder Wand is a more powerful focus of magic. Think of a wand like a magnifying glass, and then the Elder wand is a VERY powerful one. It also has the ability to be compatible with anyone.

TL;DR - Both knowledge and magical reserves have a part to play in "power" Dumbles and Volde both have a considerable amount of both.