I have this simple question, but I cannot find the answer.
I saw this video about a plane getting hit by lightning. In it, Captain Joe explains why people do not get electrocuted. This has a simple explanation, due to the Faraday cage effect produced by the fuselage. But another question come to my mind in that moment: why does the aluminum from the fuselage, that acts as a Faraday cage, not melt because of the extreme currents carried by the lightning?
After this, I thought about the following example: A thin metal (correctly grounded) lightning rod is almost intact after a strike, while a tree breaks in the middle and sometimes it even burns:
Clearly it has something to do with the resistivity of each material, much higher in the tree's wood.
It is also said in this article that the only dangerous zone a plane can get hit "is the radome (the nose cone), as it's the only part of a plane's shell that's not made of metal". So it clearly has something to do with the conductive properties of the fuselage.
So my question is basically this: why does a tree break and burn when struck by lightning but a lightning rod does not?
And, ultimately: why does a plane hit by lightning not melt with the hundreds of thousands Amperes going through the fuselage?