iPhone is not showing on Mac or iTunes

The situation is a little more complicated than that, I simplified it for the sake of the post. While it is true I have my iphone synced with a Macbook Pro, it is not my own, it is my sister's. I do not have a personal computer, however my parents bought an iMac for family use at home. My situatiion remains the same, as I don't have access to my sister's laptop because we are both busy college students.

I would like the iMac to be the new primary device for my iPhone to connect to. The iMac nor iTunes are identifiying the iphone as a device, though when I connect said iPhone it does charge.

Thank you for your help but after my sister came back home, we discovered it was the cable that was not working. Even though it registered as charging, it was not connecting to any computer's iTunes.