Question

Birds resting on high-voltage power lines are a common sight. the copper wire on which a bird stands is 1.28 cm in diameter and carries a current of 149

a. if the bird's feet are 4.12 cm apart, what is the potential difference across its body? copper's resistivity is 1.68 × 10−8 ω m . answer in units of µv.

Answer 1

Answer:

$8\cdot 10^{-4} V$

Explanation:

First of all, let's find the cross-sectional area of the copper wire. The radius of the wire half the diameter:

$r=\frac{d}{2}=\frac{1.28 cm}{2}=0.64 cm=6.4\cdot 10^{-3} m$

So the area is

$A=\pi r^2 = \pi (6.4\cdot 10^{-3} m)^2=1.29\cdot 10^{-4} m^2$

Now we can calculate the resistance of the piece of copper wire between the bird's feet, with the formula:

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

where

$\rho=1.68\cdot 10^{-8} \Omega m$ is the resistivity of copper

$L=4.12 cm=4.12 \cdot 10^{-2} m$ is the length of the piece of wire

$A=1.29\cdot 10^{-4} m^2$ is the cross-sectional area

Substituting, we find

$R=(1.68\cdot 10^{-8} m^2)\frac{4.12\cdot 10^{-2} m}{1.29\cdot 10^{-4} m^2}=5.4\cdot 10^{-6} \Omega$

And since we know the current in the wire, I=149 A, we can now find the potential difference across the body of the bird, by using Ohm's law:

$V=IR=(149 A)(5.4\cdot 10^{-6} \Omega)=8\cdot 10^{-4} V$