The resistivity of silver is 1.59 × 10-8 Ω·m. What is the resistance of a section of 12 gauge wire (diameter 0.2057 cm) that is 8.60 m long?
To calculate the resistance of a section of wire, we can use the formula:
Resistance = (Resistivity * Length) / Cross-sectional Area
First, let's calculate the cross-sectional area of the wire. The diameter of the wire is given as 0.2057 cm, but we need to convert it to meters:
Diameter = 0.2057 cm = 0.2057 * 10^(-2) m = 2.057 * 10^(-3) m
Now, we can calculate the radius:
Radius = Diameter / 2 = 2.057 * 10^(-3) m / 2 = 1.0285 * 10^(-3) m
Next, we can calculate the cross-sectional area:
Cross-sectional Area = π * Radius^2 = π * (1.0285 * 10^(-3))^2 = π * 1.057 * 10^(-6) m^2
Now, we can substitute the values into the resistance formula:
Resistance = (1.59 × 10^(-8) Ω·m * 8.60 m) / (π * 1.057 * 10^(-6) m^2)
Calculating this equation will give us the resistance of the section of wire.
To find the resistance of a section of wire, you can use the formula:
R = (ρ * L) / A
Where:
R is the resistance
ρ is the resistivity
L is the length of the wire
A is the cross-sectional area of the wire
First, let's convert the diameter of the wire to meters:
diameter = 0.2057 cm = 0.002057 m
The formula for the area of a circle is:
A = π * r^2
Since we have the diameter, we can find the radius (r) by dividing it by 2:
r = diameter / 2 = 0.002057 m / 2 = 0.0010285 m
Now, let's calculate the area of the wire:
A = π * r^2 = π * (0.0010285 m)^2
Next, plug in the values into the resistance formula:
R = (1.59 × 10^-8 Ω·m * 8.60 m) / (π * (0.0010285 m)^2)
Now, we can solve the equation using a calculator to find the resistance.