A 100 m long copper wire (resistivity 1.70x10-8Ωm) has diameter of 1.50 mm. If the current in the wire is 15 A, what is the potential difference between the ends of the wire?
To find the potential difference between the ends of the wire, we can use Ohm's Law, which states that the potential difference (V) across the wire is equal to the current (I) multiplied by the resistance (R).
First, we need to calculate the resistance of the wire using the formula:
R = (ρ * L) / A
Where:
ρ is the resistivity of the copper wire (1.70x10-8 Ωm)
L is the length of the wire (100 m)
A is the cross-sectional area of the wire (π * r^2)
Given that the diameter of the wire is 1.50 mm, we can calculate the radius (r) by dividing the diameter by 2:
r = 1.50 mm / 2 = 0.75 mm = 0.75 x 10^-3 m
Now we can calculate the cross-sectional area (A):
A = π * (r^2) = π * (0.75 x 10^-3 m)^2
Next, we can substitute the given values into the formula:
R = (1.70 x 10^-8 Ωm * 100 m) / (π * (0.75 x 10^-3 m)^2)
Simplifying this equation will give us the resistance value (R).
Once we have obtained the resistance, we can substitute it into Ohm's Law to find the potential difference (V):
V = I * R
Given that the current (I) is 15 A, we can multiply it by the resistance (R) to find the potential difference between the ends of the wire.