Given Information:
Radius of wire = r = 0.405 mm = 0.405×10⁻³ m
Length of wire = L = 15 m
Voltage = V = 12 V
Resistivity = ρ = 100×10⁻⁸ Ωm
Required Information:
Current = I = ?
Answer:
Current = I = 0.412 A
Explanation:
The current flowing through the wire can be found using Ohm's law that is
V = IR
I = V/R
Where V is the voltage across the wire and R is the resistance of the wire.
The resistance of the wire is given by
R = ρL/A
Where ρ is the resistivity of the wire, L is the length of the wire and A is the area of the cross-section and is given by
A = πr²
A = π(0.405×10⁻³)²
A = 0.515×10⁻⁶ m²
So the resistivity of the wire is
R = ρL/A
R = (100×10⁻⁸×15)/0.515×10⁻⁶
R = 29.126 Ω
Finally, the current flowing through the wire is
I = V/R
I = 12/29.126
I = 0.412 A
Therefore, the current through a 15.0-m long 20 gauge nichrome wire is 0.412 A.
