The resistance of 10 ft length of a 20 mil iron wire is 1.8 ohms. What is the resistivity of the iron?
resistance=rho*length/area
you have resitance, length, and diameter, solve for rho. watch units. 20 mil=.02inch.
To find the resistivity of the iron wire, we need to use the formula:
Resistivity (ρ) = (Resistance × Cross-sectional area) / Length
Given:
Resistance (R) = 1.8 ohms
Length (L) = 10 ft = 120 inches
Diameter (d) = 20 mil
First, let's convert the diameter from mil to inches:
1 mil = 0.001 inches
Therefore, the diameter (d) = 20 mil * 0.001 inches/mil = 0.02 inches
Next, we need to find the cross-sectional area (A) of the wire. The cross-sectional area of a wire is given by:
A = π * (d/2)^2
Where π (pi) is approximately 3.14159.
Plugging in the values:
A = 3.14159 * (0.02/2)^2 = 3.14159 * 0.01^2 = 3.14159 * 0.0001 = 0.000314159 square inches
Now, let's calculate the resistivity (ρ) using the formula:
ρ = (R * A) / L
Plugging in the values:
ρ = (1.8 ohms * 0.000314159 square inches) / 120 inches
Simplifying:
ρ = 0.00056668526 ohms × square inches / inches
Finally, the resistivity of the iron wire is approximately 0.00056668 ohms × square inches / inches.
Note: Resistivity is commonly expressed as ohm-meters (Ω·m) or ohms per meter (Ω/m), so you may need to convert the units if necessary.
To find the resistivity of the iron wire, we need to use the formula:
Resistivity (ρ) = (Resistance × Area) / Length
Given that the length of the wire is 10 ft (converting it to meters, we get approximately 3.048 meters), the resistance is 1.8 ohms, and the wire's thickness is 20 mils (converting it to meters, we get approximately 0.000508 meters), we can substitute these values into the formula.
So, the formula becomes:
ρ = (1.8 ohms × (π × (0.000508 meters)²)) / 3.048 meters
Now we can calculate:
ρ = 0.184 ohm-meters
Therefore, the resistivity of the iron wire is approximately 0.184 ohm-meters.