A cyllindrical copper cable carries a
current of 1200 A. There is a potential difference of 1.6×10−2 V between two points on the cable
that are 0.24 m apart. What is the radius of the cable?
To find the radius of the cylindrical copper cable, we can use the formula for electrical resistance:
Resistance (R) = (ρ * L) / A
Where:
- R is the resistance
- ρ (rho) is the resistivity of copper
- L is the length of the cable
- A is the cross-sectional area of the cable
First, let's find the resistivity of copper. The resistivity of copper is typically around 1.68 x 10^-8 Ω⋅m.
Given:
Current (I) = 1200 A
Potential Difference (V) = 1.6 x 10^-2 V
Distance (d) = 0.24 m
We can rearrange Ohm's law to find the resistance:
R = V / I
Substituting the values, we have:
R = (1.6 x 10^-2 V) / 1200 A
R = 1.33 x 10^-5 Ω
Next, we can rearrange the resistance formula to solve for the cross-sectional area (A):
A = (ρ * L) / R
Substituting the values, we have:
A = (1.68 x 10^-8 Ω⋅m * 0.24 m) / (1.33 x 10^-5 Ω)
A ≈ 3.02 x 10^-4 m^2
The cross-sectional area (A) is equal to π * r^2, where r is the radius of the cable. So we can rearrange and solve for the radius:
π * r^2 = 3.02 x 10^-4 m^2
Dividing both sides by π, we have:
r^2 = (3.02 x 10^-4 m^2) / π
Taking the square root of both sides, we can find the radius:
r ≈ √((3.02 x 10^-4 m^2) / π)
Calculating this value, we find:
r ≈ 0.0098 m
Therefore, the radius of the cylindrical copper cable is approximately 0.0098 m.
To find the radius of the cylindrical copper cable, we can use the formula for resistance:
Resistance (R) = (ρ * L) / A
where:
- ρ is the resistivity of copper
- L is the length of the cable section (0.24 m in this case)
- A is the cross-sectional area of the cable
We can rearrange this formula to solve for A:
A = (ρ * L) / R
Given that there is a potential difference (V) of 1.6 × 10^(-2) V across the cable and the current (I) is 1200 A, we can use Ohm's law to find the resistance:
R = V / I
Let's substitute the values into the equation to find the resistance:
R = (1.6 × 10^(-2) V) / 1200 A
Simplifying this expression gives us the resistance.
Now we need to know the resistivity of copper. The resistivity of copper is approximately 1.68 × 10^(-8) Ω·m.
Now that we have the resistance and the resistivity, we can calculate the cross-sectional area (A):
A = (ρ * L) / R
Substituting the values into the equation will give us the cross-sectional area.
Finally, we can use the formula for the area of a circle to find the radius (r) of the cable:
A = π * r^2
Rearranging the equation gives us:
r = sqrt(A / π)
Substituting the value of A, we can solve for the radius.
Look up the resistivity of copper. I will call the property r. The units should be ohm-meters.
Then use the formula
R = r*L/A
to solve for A, the area of the circular cross section
In this case, Ohm's law tells you that
R = V/I = 1.6*10^-2/1200 = 1.33*10^-5 ohms
For the radius R, use A = pi R^2