The substation bus bar is made up of 2-iches round copper bars 20 ft. long. What is the resistance of each bar if resistivity is 1.724 x 10-6 ohm-cm.
5.185 x 10-5 ohm
To calculate the resistance of each copper bar, we can use the formula:
Resistance = (Resistivity x Length) / Area
First, let's calculate the area of each copper bar.
The formula to calculate the area of a round copper bar is:
Area = π x radius^2
Given that the diameter of the copper bars is 2 inches, we can calculate the radius:
Radius = diameter / 2 = 2 inches / 2 = 1 inch
Converting the radius to centimeters:
1 inch = 2.54 cm
Radius = 1 inch x 2.54 cm/inch = 2.54 cm
Now, let's calculate the area:
Area = π x (2.54 cm)^2
Next, we need to convert the length of the copper bars from feet to centimeters:
1 foot = 30.48 cm
Length = 20 ft x 30.48 cm/ft
Now, we have all the values we need to calculate the resistance:
Resistance = (Resistivity x Length) / Area
Resistance = (1.724 x 10^-6 ohm-cm) x (20 ft x 30.48 cm/ft) / [π x (2.54 cm)^2]
Simplifying the equation will give us the final answer.
To calculate the resistance of each copper bar in the substation bus bar, you can use the formula:
R = (ρ * L) / A
Where:
R = Resistance
ρ = Resistivity of copper (1.724 x 10^-6 ohm-cm)
L = Length of the copper bar (20 ft. or converted to cm)
A = Area of the copper bar (cross-sectional area)
First, let's convert the length of the copper bar from feet to centimeters:
1 ft. = 30.48 cm
So, 20 ft. = 20 * 30.48 = 609.6 cm
Next, we need to calculate the cross-sectional area of the copper bar. Since it is round, we can use the formula for the area of a circle:
A = π * r^2
Where:
A = Area
π = Pi (approximately 3.14159)
r = Radius (half of the bar's diameter)
Given that the diameter of the bar is 2 inches, the radius is half of that:
Radius = 2/2 = 1 inch
Since the radius is given in inches, we need to convert it to centimeters:
1 inch = 2.54 cm
Now we can calculate the cross-sectional area:
A = π * (1.54 cm)^2
Finally, we can substitute the values into the resistance formula to find the resistance of each copper bar:
R = (ρ * L) / A
R = (1.724 x 10^-6 ohm-cm * 609.6 cm) / (π * (1.54 cm)^2)
Calculating this will give you the resistance value of each copper bar in ohms.