What is the length of copper wire is required to produce a 4mohm resistor? Assume the diameter of the wire is 1mm and that the resistivity roh copper is .0000000178ohmm
R = pL/A.
A = pi*r^2 = 3.14*(1/2)^2 = 0.7854 mm^2
4 = 1.78*10^-4*L/0.7854.
4 = 2.2664*10^-4L,
L = 1.765*10^4 mm = 17.65 m.
To find the length of copper wire required to produce a 4mohm resistor, we can use the formula:
Resistance (R) = (Resistivity (ρ) * Length (L)) / (Area (A))
Given the resistivity (ρ) of copper as 0.0000000178 ohmm, and the desired resistance (R) as 4 mohm (or 0.004 ohm), we need to calculate the area (A) and then solve for the length (L) of the wire.
The formula for the area of a circle is:
Area (A) = π * (radius)²
Given the diameter of the wire as 1 mm, the radius (r) can be calculated as half of the diameter:
Radius (r) = diameter / 2 = 1 mm / 2 = 0.5 mm = 0.0005 m
Now, we can substitute the values into the area formula:
Area (A) = π * (0.0005)² ≈ 0.0007854 mm²
Since 1 mm² is equal to 1e-6 m², we can convert the area to square meters:
Area (A) = 0.0007854 mm² * 1e-6 m² / mm² ≈ 7.85e-10 m²
Now, we can rearrange the resistance formula to solve for the length (L):
L = (R * A) / ρ
Substituting the known values:
L = (0.004 ohm * 7.85e-10 m²) / 0.0000000178 ohmm
L ≈ 0.01768 m ≈ 17.68 mm
Therefore, a length of approximately 17.68 millimeters of copper wire is required to produce a 4mohm resistor with a diameter of 1mm and a resistivity of 0.0000000178 ohmm.
To determine the length of the copper wire required to produce a 4mΩ (milliohm) resistor, we can use the formula for resistance:
Resistance = (Resistivity * Length) / (Cross-sectional Area)
Rearranging the formula, we can solve for the length:
Length = (Resistance * Cross-sectional Area) / Resistivity
The cross-sectional area of the wire can be calculated using the formula for the area of a circle:
Area = π * (Radius)^2
In this case, the diameter of the wire is given as 1mm, so the radius (r) can be found by dividing the diameter by 2:
Radius = 1mm / 2 = 0.5mm = 0.0005m
Now we can substitute the values into the formulas to find the length of the wire:
Cross-sectional Area = π * (0.0005m)^2 = 0.0000007854m^2
Length = (0.004Ω * 0.0000007854m^2) / 0.0000000178Ωm = 0.222m
Therefore, approximately 0.222 meters (or 22.2 cm) of copper wire would be required to produce a 4mΩ resistor with a wire diameter of 1mm and a resistivity of 0.0000000178Ωm.