RACH RA-RNTI calculation

Hi experts

In this picture specifically in the yellow part you will see the equation that the gnb uses to calculate the ra-rnti

RA-RNTI= 1 + s_id + 14 × t_id + 14 × 80 × f_id + 14 × 80 × 8 × ul_carrier_id (I copied it because it’s not clear in yellow)

My question is how does the gnb now the ul-carrier-id, fid, sid, tid Does ue need to explicitly send it to gnb so that gnb can calculate the ra-rnti?
And one more question, why do we need different RA-RNTI for different ul carriers? It’s the same UE so I’m confused why we would need to differentiate it for different carriers?