I've been googling for hours and went through over a hundred answers. Now, some say the bird doesn't form a closed loop, some say the current is so small that it doesn't kill the bird. From as much as I understand electricity, I'm sure the bird does make a parallel connection to the wire, so there must be some electrons moving through it's body.
Could someone please explain which is the right answer and why? And if it's the case that a parallel circuit is formed, how can I calculate the current going through the birds body?
Best Answer
The copper cable inside the telephone wire has some finite resistance per unit length, call it $\alpha$. If current $I_0$ is flowing through the wire, then the voltage drop across a length $L$ of cable is $V=I_0\alpha L$. Here $L$ is the distance between the bird's feet. The bird forms a parallel branch whose resistance $R$ is probably almost entirely due to the resistance of the insulator on the wire under the bird's feet, not the bird's body itself. The current though the bird is $I_B=V/R=I_0\alpha L/R$. Because $\alpha$ is small and $R$ is large, this current is extremely small compared to $I_0$.
The people who tell you $I_B$ is zero are basically right. They're applying approximations that are excellent in most situations and that are excellent in this situation. Specifically, we normally take $\alpha\approx0$ for a wire, so there is no voltage drop between any two points on the same wire.