According to the wiki, powered activator rails disable the hopper minecart's ability to pick up items from other hoppers or chests, until the minecart runs over an unpowered activator rail.
This isn't the case, however. The hopper minecart picks up items if the activator rail is powered or not.
How to reproduce:
Create a circle track similar to the one in the screenshot. Make sure that both the activator rail and powered rails are powered
Put any amount/type of item in the hopper above the rail
Send the hopper minecart on its way.
Check the hopper underneath the rail for items.
What to expect:
There shouldn't be any items in the lower hopper or the hopper minecart.
What actually happens:
The hopper minecart transports the items from one hopper to the other.
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@ItsRichHeart what you have said is incorrect. Powered activator rails disable hopper minecarts not just when they are sitting on the activator rail, but until they run over an unpowered activator rail.
@John Smith in the setup in your picture, the reason items are moving is that the hopper above the rails is still able to push items, and the hopper below the rails is still able to pull items. You would get the same item movement if you used a minecart with chest, which has no ability to push or pull on its own. Try replacing the hoppers with chests, barrels, droppers, etc., or power the hoppers to disable them, and then run your hopper minecart around the track, and you should see the effect of the activator rail.
Hopperminecart wont pick up items when they are on a powered activaterrail. In your screenshot the hopperminecart will deposit his items because there is no powered activaterrail