How much current will be flowing through a 57.0m length of copper wire with radius 5.7mm if it is connected to a source supplying 620V.
(The resistivity of copper is 1.68x10^-8ohm's.m
To determine the current flowing through the copper wire, we will need to use Ohm's law and the formula for resistance.
The formula for resistance is as follows:
R = (ρ * L) / A
Where:
R = resistance
ρ = resistivity of copper (given: 1.68x10^-8 ohm's.m)
L = length of the wire (given: 57.0m)
A = cross-sectional area of the wire
The cross-sectional area of a wire can be calculated using the formula:
A = π * r^2
Where:
A = cross-sectional area
r = radius of the wire (given: 5.7mm = 0.0057m)
So, let's calculate the cross-sectional area first:
A = π * (0.0057m)^2
A ≈ 3.2415 x 10^-5 m^2
Now we can calculate the resistance of the wire:
R = (1.68x10^-8 ohm's.m * 57.0m) / (3.2415 x 10^-5 m^2)
R ≈ 2.9536 x 10^-5 ohms
Finally, we can apply Ohm's law to calculate the current:
V = I * R
Where:
V = voltage (given: 620V)
I = current
Solving for I:
I = V / R
I = 620V / 2.9536 x 10^-5 ohms
I ≈ 2.1003 x 10^7 amps
Therefore, the current flowing through the 57.0m length of copper wire will be approximately 2.1003 x 10^7 amps.
To calculate the current flowing through the copper wire, we need to use Ohm's Law, which states that the current (I) flowing through a conductor is equal to the voltage (V) applied across the conductor divided by the resistance (R) of the conductor.
The resistance of the copper wire can be calculated using the formula:
R = (rho * L) / A
Where:
rho - resistivity of copper (1.68x10^-8 ohm's.m)
L - length of the wire (57.0m)
A - cross-sectional area of the wire
To calculate the cross-sectional area, we need to use the formula:
A = pi * r^2
Where:
r - radius of the wire (5.7mm or 0.0057m)
pi - mathematical constant approximately equal to 3.14159
First, let's calculate the cross-sectional area:
A = pi * (0.0057m)^2
Once we have the cross-sectional area, we can calculate the resistance:
R = (1.68x10^-8 ohm's.m * 57.0m) / (pi * (0.0057m)^2)
After calculating the resistance, we can apply Ohm's Law to find the current flowing through the wire:
I = V / R
Where:
V - voltage supplied by the source (620V)
R - resistance of the wire
Now, let's substitute the values into the formulas and calculate:
A = 3.14159 * (0.0057m)^2 = 1.02713x10^-4 m^2
R = (1.68x10^-8 ohm's.m * 57.0m) / (3.14159 * (0.0057m)^2) = 0.51314 ohms
I = 620V / 0.51314 ohms
The current flowing through the copper wire will be approximately:
I = 1207.22 Amperes.