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 find the resistance of a section of wire, we can use the formula:
Resistance (R) = (Resistivity x Length) / Cross-sectional Area
Where:
- Resistivity (ρ) is the property of a material that quantifies how strongly it resists the flow of electric current.
- Length (L) is the length of the wire section.
- Cross-sectional Area (A) is the area of the wire section through which the current flows.
First, we need to convert the diameter of the wire to radius, which is half the diameter:
Radius (r) = Diameter / 2
In this case, the diameter is 0.2057 cm, so:
Radius (r) = 0.2057 cm / 2 = 0.10285 cm
Next, we need to convert the radius to meters:
Radius (r) = 0.10285 cm × (1 m / 100 cm) = 0.0010285 m
Now, we can calculate the cross-sectional area of the wire using the formula for the area of a circle:
Cross-sectional Area (A) = π × (Radius)²
Substituting the values:
Cross-sectional Area (A) = π × (0.0010285 m)²
Using the value of π ≈ 3.14159:
Cross-sectional Area (A) ≈ 3.14159 × (0.0010285 m)²
Now, we can plug the values of resistivity, length, and cross-sectional area into the formula to find the resistance:
Resistance (R) = (1.59 × 10^(-8) Ω·m × 8.60 m) / (3.14159 × (0.0010285 m)²)
Calculating this expression will give us the resistance of the wire section.