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I have installed a 75 amp sub panel with three #6THHN and a #8 ground from the main. I need to move two branch circuits from main to sub since I do not have space in the 200amp main for the sub panel breaker.
Is a ground wire required for each branch circuit if they are in the same conduit as the feeders for the sub? One inspector said that each circuit has to have a ground. It seems redundant.
All the branch circuits in a single cable or conduit can share a single ground wire (and are often forced to when metal conduit is used as a ground path or when a multi-circuit cable is used). This is permitted as a consequence of NEC 250.122(C):
(C) Multiple Circuits. Where a single equipment grounding conductor is run with multiple circuits in the same raceway, cable, or cable tray, it shall be sized for the largest overcurrent device protecting conductors in the raceway, cable, or cable tray. Equipment grounding conductors installed in cable trays shall meet the minimum requirements of 392.10(B)(1)(c).
Several circuits in the same conduit CAN share a ground wire that's big enough for the biggest of them.
This here is the main issue, that I think is driving people to tell you you need separate grounds.
So you have 2 different things in the same pipe. #1 you have a feeder sourced at the main panel going to the subpanel. It needs a ground wire coming out of the main panel.
And #2 you have multiple circuits sourced from the subpanel. Their ground needs to come out of the subpanel.
So yes, you have two grounds who "pass like ships in the night".
OK. Presuming both panels are connected by non-flexible metal conduit, that is allowed to serve as the ground, so you don't need any ground wires at all. In this case, the metal conduit is allowable for the ground for the feeder, and also allowed for the ground for the branch circuits. So you're all set.
However, what do you do with the subpanel circuits' grounds; it seems weird to take them to a main panel's ground bar, since that resembles the thing you're not supposed to do. Just to avoid inspector redflags, I would extend off either panel with a short (<24") length of metal conduit to a junction box. Put a ground pigtail on the box. Reroute the subpanel circuits to enter the junction box instead of the main panel, and tap its ground.
I notice you said "75 amp panel". As a rule, those panels are terribly small - 6 or 8 spaces. You have already been given a lesson about "running out of spaces" and I hope you took it to heart. Many of us advise VERY, like "insanely", large panels. The cost of the additional spaces is very low compared to both total project cost, and inconvenience cost if you run out of spaces again. I for one like to see total breaker spaces in a house to be in the forties. So if you have a 16 space/32 circuit, add a 30-space. Etc.
While of course there is always another load, and it improves life to be able to handle any future load easily, it also allows you to "un-double-stuff" the old panel, which has typically been double-stuffed before this point. This is necessary for future fitting of AFCI or GFCI.
Lastly, you are not allowed to use the 90C temperature column in the cable ratings. Generally you are in the 60C column, or 75C if several conditions are met. Most likely the supply breaker and subpanel lugs are rated for 75C, and THHN in conduit is good for 75C (actually 90C). So you can use the 75C column, giving 65A for your #6Cu THHN. You can then "round up" to the next breaker size of 70A.
