Final answer:
The resistance of a wire can be calculated using the formula R = (ρ x L) / A, where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire. To find the resistance, we need to determine the resistivity and cross-sectional area of the wire. The resistivity of copper is approximately 1.68 x 10^-8 ohm-meter.
Step-by-step explanation:
The resistance of a wire can be calculated using the formula:
R = (ρ x L) / A
Where:
- R is the resistance of the wire
- ρ (rho) is the resistivity of the material
- L is the length of the wire
- A is the cross-sectional area of the wire
To find the resistance, we need to determine the resistivity and cross-sectional area of the wire. The resistivity of copper is approximately 1.68 x 10^-8 ohm-meter. The cross-sectional area of a circular wire can be calculated using the formula:
A = π x (r^2)
Where:
- A is the cross-sectional area of the wire
- π (pi) is a constant approximately equal to 3.14159
- r is the radius of the wire, which can be calculated by dividing the diameter by 2
Once we have the resistivity and cross-sectional area, we can calculate the resistance using the formula.
Let's plug in the values:
Diameter = 2.1 mm = 0.0021 m
Radius = 0.0021 m / 2 = 0.00105 m
Cross-sectional area (A) = π x (0.00105^2)
Resistance (R) = (1.68 x 10^-8 ohm-meter x length) / (π x (0.00105^2))
Given that the current is 6.7 mA, which is equivalent to 0.0067 A, we can rearrange the formula to find the length of the wire:
Length (L) = (Resistance x Cross-sectional area) / (Resistivity x Current)
Plugging in the values, we get:
Length = (R x A) / (ρ x I)
Length = (R x π x (0.00105^2)) / (1.68 x 10^-8 ohm-meter x 0.0067 A)
Simplifying the equation will give us the length of the wire.
Using the given options, we can calculate the resistance for each:
a. 4.164 ohms
b. 0.013 ohms
c. 6.733 ohms
d. 0.417 ohms
By comparing the calculated resistance with the options, we can determine the correct resistance value.
Therefore, the correct answer is option b. 0.013 ohms