A nichrome wire has a radius of 0.50 mm and a resistivity of 1.5 ´ 10‑6 W‑m. What is the resistance per unit length of this wire?
0.00015 ohm
To find the resistance per unit length of the nichrome wire, we can use the formula for the resistance of a cylindrical wire:
R = (ρ * L) / A
Where:
R is the resistance
ρ (rho) is the resistivity of the material
L is the length of the wire
A is the cross-sectional area of the wire
In this case, we are given the radius of the wire (0.50 mm), but we need the cross-sectional area. To find that, we use the formula:
A = π * r^2
Where:
A is the cross-sectional area
π (pi) is a mathematical constant approximately equal to 3.14159
r is the radius of the wire
Now, let's calculate the cross-sectional area of the wire:
A = π * (0.50 mm)^2
A = π * (0.0005 m)^2
A ≈ 3.14159 * (0.0005 m)^2
A ≈ 3.14159 * 0.00000025 m^2
A ≈ 7.85475 × 10^-7 m^2
Now we can substitute the values we know into the resistance formula:
R = (1.5 × 10^-6 W-m * L) / (7.85475 × 10^-7 m^2)
To find the resistance per unit length, we divide both sides of the equation by L:
R/L = (1.5 × 10^-6 W-m) / (7.85475 × 10^-7 m^2)
Simplifying the expression:
R/L ≈ 1.9098593 Ω/m
Therefore, the resistance per unit length of the nichrome wire is approximately 1.9099 Ω/m.