The human body isn’t a simple ohmic resistor. At low voltages, the human body has a fairly high resistance, several hundred thousand ohms or higher. At higher voltages, the effective resistance of the human body can easily drop to under 1,000 ohms. One of the more common electrical models of the human body is a resistor in series with a resistor and capacitor in parallel. However, the values of those components changes based on the voltages involved (it’s also an admittedly very much over-simplified model).
Electricity usually tends to kill you in one of two ways.
At lower current levels, the electricity interferes with your heart’s rhythm. It takes a surprisingly small amount of current to potentially screw up your heart. U.S. safety standards tend to be built around 5 mA (0.005 amps) being the “safe” level. Anything above that could kill you. The thing about this though is that it’s a bit hit and miss. Your heart is much more sensitive to disruption at certain times during its cycle than others, so a lot depends on exactly when the shock occurs and where the heart is in its cycle at the time. Hit it at just the right time, though, and the heart goes into fibrillation. Your heart has kind of a funny design in that the fibrillation state is stable. In other words, the heart will happily stay in fibrillation and won’t go back into a normal rhythm unless something else happens (like someone whacks it back into rhythm with a portable defibrillator). In fibrillation, your heart just sits there and shakes chaotically. Since it’s effectively not pumping blood, you pass out quickly and die shortly thereafter.
As the current increases, at first the risk of fibrillation increases along with it, but then a funny thing happens. Once you reach a certain current level, instead of going into fibrillation, the heart muscles all just kinda clamp. At that point the heart isn’t pumping blood, so you are still in a world of hurt unless someone removes the source of the electrical current, but once the current is removed, the heart usually goes back into a normal rhythm all by itself.
Above this current level, the second type of effect kicks in, and you are literally burned to death. The electricity heats up your body and burn damage kills you. This is how the electric chair kills. Electric chairs also tend to work at voltages around 2,000 to 4,000 volts, so they are on the low end of what your typical distribution line would have on it, if you want to put that in perspective. Burn damage is a lot less hit and miss than fibrillation, but some of the survivability does depend on exactly the path that the current takes through your body.
If you haven’t watched the video that GaryM linked to upthread, it’s a really good example of just what a few thousand volts can do to a tree. Similar things happen to a person.
Higher voltages will also punch through thicker levels of insulation (like human skin, tree bark, etc). Trees are also non-linear resistor loads. Once the voltage gets high enough that it can punch its way into the sap, the effective resistance drops dramatically. Lightning often follows the sap down as it flows through a tree, quite often flashing the sap into steam and blowing the tree apart as a result.
Also, current doesn’t take the path of least resistance. Current takes all paths that it can find. It’s just that more current flows through the paths of lesser resistance.
Typically a transformer will supply power to only three or four houses. If you’ve got close to a dozen homes I’d expect there to be at least a couple of transformers involved. Either way, the distribution voltage could be as low as 2400 volts for that area, which wouldn’t cause as much sparking and excitement. If it’s a three-phase feed, they could probably power all of the cottages from a single three-phase transformer at the distribution end of the line. There would be three wires instead of two running out to the cottages, and each cottage would get a connection to two of the three wires (which two wires would be evenly balanced between the cottages).
I think most people are aware that dropping a tree into power lines is bad. Less people are aware of how far electricity can arc, and might think that as long as they don’t touch the wires that they are safe. I think this is why the safety literature is skewed towards arcing.
If the electricity can reach the other wire (i.e. the tree mashed the two wires together) then it will certainly want to go back along the path of the other wire, as well as wanting to go into earth ground through the tree.
