Time Capsule

You would hope not..

If you are referring to the Macbook air.. it can be slow due to the poor wireless speed.

Try just copying a file between the air and the TC and get a speed for that transfer and then estimate how long.

It will need to go through all the backup if you haven't used it for a while to check the existing backup and what it is missing.

You might almost find it is easier to wipe the TC and do a fresh backup.

I would recommend you get the best speed possible. That means using the air in the same room as the TC.. and check that wireless is joining at 5ghz and 300mbps or 450mbps for latest version air and TC.

Otherwise open the airport utility and go to wireless setup.. use SMB name.. short, no spaces pure alphanumeric and give a different name in wireless options to 5ghz so you can force the connection to use the faster link.

A USB to ethernet cable is cheap and can be well worth it.. you can get a non-apple one for <$10 but even apple one is not too bad.. Thunderbolt to ethernet even better but uber expensive.

I just set one up with a MacBook Air ...

It's not fast...even with Ethernet

23 gb was several hours...switched to Ethernet cause wireless was very slow

I do not think it is network speed that is limiting...it is much slower than that..it must be checking something...

TC works well but the one knock i have is the slowness of time machine...

When used as a hard drive it seems reasonably fast

My Time Machine backups achieve about 50-60GB per hour.. over ethernet.

On the air did you use USB to ethernet or thunderbolt to ethernet adapter??

Did you switch off wireless.. as it goes very slow when it has two possible paths.. and seems to still prefer wireless.

23GB certainly should not take several hours.

But it is worth testing where the issue lies.. try doing TM backup to an external drive plugged straight into the air.