but i found that when i turn my router off at night then turn it on in the morning i notice that the the IP address has changed

so jw would anyone know say if i turned it off now how long i would have to wait to turn it back on to find that it has given me a new ip?

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Chicken

Doesn't matter about the time.
It's instant.

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Any render of a 3D image posted by me, was by me.
So please don't ask.

Most likely you have DHCP enabled locally which distributes the IPs automatically when the computers connect, so if you restart it then another computer on the network may get your address. If you'd like the same address you should be able to turn on IP/MAC assignments so they get reserved ones, whilst still allowing DHCP on your router.

If you mean your IP address that identifies you on the Internet, well your ISP gives that out to you, and a new one is given whenever you reconnect to the Internet with your modem, so it would make sense that if you restart your router (assuming modem/router are the same device) then a new IP address is assigned to you.

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and victorious in war shall be made glorious in peace.