Question

Birds resting on high-voltage power lines are a common sight. the copper wire on which a bird stands is 3.5 cm in diameter and carries a current of 32

a. the bird's feet are 2.1 cm apart. (b) calculate the potential difference across its body.

Answer 1

`1.0 \cdot 10^(-5)V`

Step-by-step explanation:

First of all, we need to calculate the resistance of the piece of copper wire between the bird's feet, which is given by

`R=\rho (L)/(A)`

where:

`\rho = 1.68 \cdot 10^(-8) \Omega m` is the resistivity of copper

`L = 2.1 cm = 0.021 m` is the length of the piece of wire between the bird's feet

`A=\pi r^2` is the cross-sectional area of the wire, with r being the radius. Since the radius is half the diameter:

`r=(3.5 cm)/(2)=1.75 cm=0.0175 m`

the area is

`A=\pi (0.0175 m)^2=9.34 \cdot 10^(-4) m^2`

And the resistance is

`R=(1.68\cdot 10^(-8) \Omega m (0.0175 m)/(9.34 \cdot 10^(-4) m^2)=3.15\cdot 10^(-7)\Omega`

And given the current in the wire, I=32 A, we can calculate the potential difference across the bird's body by using Ohm's law:

`V=IR=(32 A)(3.15\cdot 10^(-7) \Omega)=1.0 \cdot 10^(-5)V`