A bird lands on a bare copper wire carrying a current of 27 A. The wire is 8 gauge, which means that its cross-sectional area is 0.13 cm2.
(a) Find the difference in potential between the bird's feet, assuming they are separated by a distance of 7.2 cm.
To find the difference in potential between the bird's feet, we can use Ohm's law and the concept of voltage drop.
The voltage drop (ΔV) across a wire can be calculated using the formula:
ΔV = I * R
Where:
ΔV is the voltage drop (difference in potential),
I is the current flowing through the wire,
R is the resistance of the wire.
First, we need to find the resistance of the wire using the wire's cross-sectional area and gauge.
The cross-sectional area (A) of the wire is given as 0.13 cm². To use this in our calculation, we need to convert it to square meters:
A = 0.13 cm² = 0.13 * 10^(-4) m²
The resistance (R) of the wire can be calculated using the formula:
R = ρ * L / A
Where:
R is the resistance of the wire,
ρ (rho) is the resistivity of the wire material (copper in this case),
L is the length of the wire.
The resistivity of copper is approximately 1.68 * 10^(-8) Ω·m.
However, we need to convert the length of the wire to meters before using it in the formula. Assuming the length of the wire is not given, let's assume it's 1 meter for simplicity.
L = 1 m
Now we can calculate the resistance:
R = (1.68 * 10^(-8) Ω·m) * (1 m) / (0.13 * 10^(-4) m²)
Next, we can calculate the voltage drop using Ohm's law:
ΔV = (27 A) * (R)
Finally, we can find the difference in potential between the bird's feet by using the given distance:
distance = 7.2 cm = 7.2 * 10^(-2) m
ΔV = (27 A) * (R) * (distance) / (1 m)
This calculation will give you the difference in potential between the bird's feet.
To find the difference in potential between the bird's feet, we can use Ohm's Law and the equation for voltage drop (ΔV):
ΔV = I * R
Where ΔV is the voltage drop, I is the current, and R is the resistance.
First, let's calculate the resistance of the wire using the cross-sectional area:
A = π * r^2
Where A is the cross-sectional area and r is the radius of the wire.
Given that the cross-sectional area is 0.13 cm², we can rearrange the equation to solve for the radius:
r = √(A / π)
r = √(0.13 cm² / π) ≈ 0.205 cm
Next, let's convert the radius to meters since we will be using SI units in our calculations:
r = 0.205 cm * (1 m / 100 cm) = 0.00205 m
The resistance can now be calculated using the formula:
R = ρ * L / A
Where R is the resistance, ρ is the resistivity of copper (1.7e-8 Ω·m), L is the length of the wire, and A is the cross-sectional area.
Given that the length of the wire is not provided, we'll assume a standard length of 1 meter, so L = 1 m.
Using these values, we can calculate the resistance:
R = (1.7e-8 Ω·m) * (1 m) / (0.13 cm²) = 1.31e-6 Ω
Now that we have the resistance, we can calculate the difference in potential:
ΔV = (27 A) * (1.31e-6 Ω) = 3.537e-5 V
Therefore, the difference in potential between the bird's feet is approximately 3.537e-5 volts.