HDMI cables are backward compatible, so an HDMI cable with 4K capabilities will transmit 1080p video, which is the resolution of your 1080p TV.
Can I use a 4K HDMI cable on my 1080p TV?
Can you use a 4K HDMI cable on a non 4K TV?
HDMI 1.4 – If you want your HDMI cables to support 4K resolution, you need to make sure that they are High-Speed HDMI cables. They are tested to transmit video resolutions from 1080p to 4K with a richer color palette. With or without HDR, you need High-Speed HDMI cables.