Can't Charge Phone by Connecting to iMac

Yes indeed and the connection is directly into the back of the iMac - not a hub. I would be very happy with cutting off the syncing process since I don't need a sync when I connect the two. I only connect to charge the phone. How can I cut off syncing? Which presumably would leave me with charging only and thus avoid this constant oscillating.

Yes of course, I could do that with a charger but the most convenient thing for me to do is just to plug it into the iMac and that should work. It's not a big deal but I like problem solving and I can't figure out why I am having problems with trying to charge on the iMac.

Yes - I just connected my iPad to the iMac and - Do You Trust This Computer - came up on the iPad screen. I tapped yes and the lightning bolt showed up on the iPad, indicating that it's charging and just like with the iPhone, the lightning bolt flashes and emits a small sound with each flash - exactly the same as with the iPhone. So neither device seems to be able to be charged from the iMac.

Unfortunately no and I'm not willing to buy another one just to test out whether that is the problem here. I think the issue may be that it is trying to sync and can't. Do you know what I can do to change the settings (on the iMac or the iPhone) so that when I connect the two, the phone does not try to sync?

Wow! Thank you so much! A simple solution to the problem if you know what you are doing which I obviously did not. This worked beautifully - I can now connect the phone and the iMac without all the weirdness I experienced previously and the phone just charges quietly overnight. Thanks again for your patience with all the back and forth. We got the desired result in the end.