As an AC, you should learn the relationship of voltage, to amperage, to watts. Be able to calculate one given the other two. This is helpful when calculating power draws of various cameras and accessories, and determining how long a certain battery will last. Not all batteries are smart and will tell you how much time is left. Same goes for chargers - being able to decipher to amperage being put out by a charger from that tiny label on the bottom and know it will be X hours for a full charge. Or how many block battery chargers can I put on one AC circuit before I'm getting close to tripping it? Some of the newer battery technologies out there like the LiFePO4 chemistries charge extremely fast, and their chargers draw like 7 Amps each.
Know the different battery chemistries out there - Lithium Ion, NiMh, not just theoretical pros and cons for each, but real world pros and cons. Familiarize yourself with the voltage curves of each kind of battery...on a lithium ion battery, if the voltage drops below 13V, I know it's getting close to battery swap time.
Nice to know but not totally necessary: some basic electronics components, e.g, the kinds of fuses in different electronics, whether they are self resetting, diodes, etc. E.g, if an accessory port on a camera has too much power drawn on it and it trips, it's usually self resetting if you power down and wait for the fuse to reset (it's thermal.) Or if a battery charger stops working, to check the fuse - usually a glass fuse.
Re: Sound; some basic knowledge of single system vs double system is required. On small budget stuff or doc stuff when it's single system, know how to set sound levels in the camera, know about the dB scale, headroom, etc. Phantom power. When doing double system and there is a sound department to take care of all this, learn about timecode. Again sound department will take care of it, but it serves you well to be able to navigate the menus in your camera for the right timecode settings, as not all sound recordists will know how to do that for a proper jam.