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

Answer:

$1.0 \cdot 10^{-5}V$

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

$R=\rho \frac{L}{A}$

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:

$r=\frac{3.5 cm}{2}=1.75 cm=0.0175 m$

the area is

$A=\pi (0.0175 m)^2=9.34 \cdot 10^{-4} m^2$

And the resistance is

$R=(1.68\cdot 10^{-8} \Omega m \frac{0.0175 m}{9.34 \cdot 10^{-4} m^2}=3.15\cdot 10^{-7}\Omega$

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:

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