We have no means by which we could tell.
The overwhelming majority of electricity in D&D is described in terms of what it does to a creature. The effects of electricity on a living creature don’t vary all that dramatically based on it being direct or alternating—DC will tend to stop a heart, while AC will tend to cause fibrillation, but both conditions are quickly fatal. A stopped heart is somewhat more likely to restart than a fibrillating heart (hence the defibrillator, which is basically a big DC shock to stop the heart so it can hopefully restart), but so far as I know, D&D doesn’t have any rules about defibrillation. DC also tends to freeze muscles, while AC often causes spasms, but neither is really described by any of the electrical attacks we see in the game.
Electricity also usually causes burns, which is probably the most straight-forward thing to turn into (non-fatal) “lightning damage.” But AC and DC are both going to do that about the same.
Note there’s a lot on the net about which one is more dangerous, and a lot of it is urban legend. There’s some validity to some of it—AC voltages are reported by the “root mean square” voltage, which is less than the “peak” voltage, so when your wall outlet is said to be 120 V (US) or 240 V (EU) or whatever, the peak voltage is actually higher than that, whereas DC is (by definition) always the same value. If one has a situation where x V is dangerous, an alternating current with RMS voltage lower than x may still have moments where it exceeds x. And AC can induce a current through your body in circumstances where DC could not—DC always needs a complete loop.
But none of that applies to D&D, where we don’t have measured voltages or voltage limits, and we don’t really have to care about stuff like DC needing a complete loop because magic is forcing the electricity to move in ways it wouldn’t naturally. This is the really key thing—everything we know about AC vs. DC is suspect, because magical electricity unambiguously moves in ways that don’t match how natural electricity moves. If it did, it wouldn’t go where the spellcaster wants it to go—it would just follow the path of least resistance, as electricity generally does. In most cases, that’s going to be up the caster’s arms, through his body (likely causing cardiac arrest—either by stopping or fibrillating the heart), and into the ground. That isn’t what the rules describe, and lightning magic wouldn’t be very useful if it was.
Finally, on the subject of wood, its conductivity/resistivity¹ isn’t significantly affected by whether we’re discussing alternating or direct current. I have found some mention of especially high AC frequencies causing the resistivity of wood to drop, but this isn’t the primary concern in most of the literature. Rather, the big thing about wood’s conductivity, mentioned everywhere I could find that discussed the subject, was moisture content. “Oven dry” wood is a rather good insulator—it has high resistivity/low conductivity. But damp wood can conduct electricity quite fairly well.
Again, though, none of that matters much to magical electricity, though—because magic is forcing the electricity to go to places it wouldn’t otherwise. If magic is forcing it through the wood, it’s going to go through the wood even if some other path of lesser resistance is available. The only real question, basically, is how much power it’s going to take—and consequently, how hot the wood is going to get. Which, in D&D terms, is presumably related to how much lightning damage is being dealt. But since that’s abstracted to a fixed value, it would seem that perhaps magical electricity doesn’t even maintain that relationship.
- Resistivity (ρ) and conductivity (σ) are inverses of one another, ρ = ¹⁄σ and σ = ¹⁄ρ, so really we’re talking about the same physical attribute, just different ways of looking at it.