a plain carbon steel wire 3mm in diameter is to offer a resistance of no more than 20 ohms carbon has a conductivity of 0.6*10*7.calculate the maximum wire length
To calculate the maximum wire length, we need to use the resistivity formula:
Resistance = (resistivity x length) / cross-sectional area
Given:
Resistance (R) = 20 ohms
Resistivity (σ) = 0.6 x 10^(-7) Ω.m (conductivity of carbon)
Cross-sectional area (A) = πr^2 (where r is the radius, which is half the diameter)
First, we need to find the radius:
Diameter = 3 mm = 0.003 m
Radius (r) = 0.003 / 2 = 0.0015 m
Now, we rearrange the resistivity formula to solve for length:
Length = (Resistance x cross-sectional area) / resistivity
Substituting the given values:
Length = (20 * π * (0.0015)^2) / (0.6 x 10^(-7))
Calculating:
Length = (0.0942) / (0.6 x 10^(-7))
Length ≈ 1.57 x 10^5 meters
Therefore, the maximum wire length should be approximately 157,000 meters.
To find the maximum wire length of a plain carbon steel wire with a diameter of 3mm that offers a resistance of no more than 20 ohms, we need to use the formula for resistance:
Resistance (R) = (ρ x L) / A
Where:
R = Resistance
ρ = Resistivity
L = Length of the wire
A = Cross-sectional area of the wire
In this case, we are given the resistance (R) and the diameter of the wire. We can use the diameter to calculate the cross-sectional area (A). Let's break down the steps:
Step 1: Calculate the radius of the wire.
The radius (r) can be found by dividing the diameter by 2.
r = 3mm / 2 = 1.5mm = 0.0015m
Step 2: Calculate the cross-sectional area (A).
The cross-sectional area of a wire is given by the formula: A = π * r^2.
A = π * (0.0015m)^2
Step 3: Calculate the maximum length (L).
Using the given resistivity (ρ) and maximum resistance (R) values, we can rearrange the resistance formula to solve for the length (L).
L = (R * A) / ρ
Let's plug in the values into the formulas and calculate the maximum wire length:
Step 1:
r = 0.0015m
Step 2:
A = π * (0.0015m)^2
Step 3:
L = (20 ohms * A) / (0.6 * 10^-7)
Now, we can calculate the maximum wire length.
well, consider the units.
Ω/m * m = Ω