From the Super Mario Wiki
The Big Amps (or Mega Amp) are large sub-species of Amps. They first appeared in Mario Party 5. Regardless of their size, they have the same designs (excluding Super Mario Galaxy). They are redesigned in New Super Mario Bros. U, looking similar to the normal-sized ones from New Super Mario Bros. Wii, though they are few times bigger.
Super Mario series
Super Mario Galaxy
Big Amps appear in Super Mario Galaxy as faceless orbs unlike the regular-sized ones. Despite that, they will still act the same way as in the other games, and they will move as well.
Super Mario Galaxy 2
Big Amps return in the sequel to Super Mario Galaxy, Super Mario Galaxy 2. They appear in the Space Storm Galaxy.
New Super Mario Bros. U
Big Amps make their Wii U debut in New Super Mario Bros. U. They behave exactly like normal sized Amps, except they are few times bigger. There are plenty of them in Snake Block Tower alongside their original counterpart. If Mario touches one, he will be electrocuted.
They're one of the very few enemies not to return in New Super Luigi U.
Mario Party series
Mario Party 5
Big Amps first appear in Mario Party 5. They appear in Shock Absorbers, along with their normal sized Amps. At first, they are a little bit bigger than a normal Amp. Touching them will electrify the player.
Mario Party 6