Use the ampacity tables to select the cable corresponding to the breaker size with a 30 amp breaker requiring a 10 3 cable a 40 amp breaker an 8 3 cable and a 50 amp breaker a 6 3 cable.
Solar backfeed breaker size.
To calculate the fuse size required between the string and the inverter s dc input you take 9 12 x 1 56 14 7 and round up to the next trade size of 15a.
Understand that corresponds to 32a of pv current maximum.
We sometimes see people adding a 60 or 80 a breaker instead.
I am not a code expert or electrician.
The sizing of back feed breakers is another point of difficulty.
The nec allows adding a back feed breaker so that the current supply is up to 120 of the rating of the bus bar.
If a 200 a busbar has a 200 a main breaker the code allows adding a up to a 40 a backfeed breaker.
Having said that a 200a rated panel with a 200a main breaker would allow up to 40a of backfeed breakers placed at the opposite end of the panel busbars from the main breaker.
Select the breaker size that can carry the current with common breaker sizes being 30 amps 40 amps or 50 amps.
Then looking at that photo again you can see i have a 30a 2 pole breaker at the other end for my solar inverter.