I recently moved and no longer wish to use my time capsule as a wifi router (wifi is supplied at the I recently moved and no longer wish to use my time capsule as a wifi router (wifi is supplied at the new place). How do I set up my time capsule to w

Is it possible to just use the internet wirelessly through the iMac and connect the time capsule with either an ethernet cable

Yes.. this is possible.. it is not the easiest configuration.. but as long as wireless network is using a different IP range.. lets say 192.168.x.x then you can plug the TC by ethernet into the Mac and simply make sure wifi is above ethernet in priority here.

or even a USB cable to simply run backups on the iMac itself?

USB will not work.. the TC is a network device.

But if you are prepared to use USB disk.. don't use the TC.. buy a standard USB drive and plug it into the Mac and use that for backup.. it is much faster and far more reliable than backups over network.

The difficulty with TC plugged directly to the Mac is your Macbook Pro cannot connect to the TC unless you also plug in ethernet cable to laptop.. later Mac laptops have no native ethernet so you need to buy a dongle.

If you do buy a USB drive for the Mac it is possible to share that to the network as a backup target. This will then work over the standard wifi. Sell the TC as it is no longer required.

Only with High Sierra and above.

https://www.howtogeek.com/330288/how-to-set-up-your-mac-to-act-as-a-networked-time-machine-drive/

The TC could plug into the main wireless router by ethernet.. with wireless off and set in bridge as nothing more than a dumb hard disk on the network.. but you need to access it then over wifi on both Macs.

It will come down to do you want to have to change networks between accessing the Internet or running Time Machine backups with your current equipment.

If not, then do you have administrator access to the wireless router that is providing you your Wi-Fi network at your new location?

The Time Capsule cannot connect to a 3rd party WiFi network using only a wireless connection. It must connect to the network router using a permanent, wired Ethernet cable connection.

So, the first question to clarify here is......Do you have physical access to the WiFi router that is providing the wireless service at your new location?

Assuming that you do have physical access to the WiFi router, are you willing or able to connect the Time Capsule to that device using a permanent, wired Ethernet cable connection?

Once we have an answer to that question, we may have an unusual type of alternate option for you to consider. The downside.......this option will require that you already have a spare AirPort Express to repurpose......or....... you have the ability to purchase and add this type of device.

I do have physical access to the router but don't particularly want to change their setup or configuration (it's my daughter's house) if it's not necessary.

No changes at all will be necessary to any of the settings on the main router if you have an interest in my current suggestion, which would be to connect the Time Capsule to the router using a wired Ethernet cable connection, turn off the WiFi on Time Capsule, and use the main router's WiFi to back up to Time Capsule from both the iMac and MacBook Pro.

This way, both the iMac and MacBook can stay connected to the main router WiFi network, and backups will occur seamlessly and automatically.

Post back if you are interested in this type of setup and you need a few tips on how to set things up.

Then at this point, we will need to first check to see if you can access the Time Capsule to take a look at the current settings on the device......in which case, it will only take a few edits to set up the Time Capsule.

Temporarily, turn off the WiFi on the iMac and connect an Ethernet cable from the iMac to one of the three LAN <--> ports on the Time Capsule.

Power up the Time Capsule and give it a few minutes to stabilize

Then, open AirPort Utility on your iMac (Finder > Applications > Utilities > AirPort Utility) and check to see if the picture of the Time Capsule appears

If it does, click on the picture of the Time Capsule and a smaller window will appear

Click Edit in that smaller window to reveal the current network settings for the Time Capsule with tabs at the top of the window for Base Station, Internet, Wireless, Network, etc.

Report back on your progress and findings, so we can tell you which settings to check and/or change.