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?
1.9 olms/m
To find the resistance per unit length of the nichrome wire, we can use the formula:
Resistance per unit length (R) = (resistivity x length) / (cross-sectional area)
Given:
- Radius of the wire (r) = 0.50 mm = 0.00050 m
- Resistivity of the wire (ρ) = 1.5 x 10^-6 Ω-m
We need to find the resistance per unit length, so let's assume the length of the wire is 1 meter (L = 1 m).
First, we need to find the cross-sectional area (A) of the wire using the formula:
Cross-sectional area (A) = π x r^2
Plugging in the values:
A = π x (0.00050 m)^2
A = 3.14 x (0.0000025 m^2)
A = 7.85 x 10^-6 m^2
Now we can calculate the resistance per unit length (R) using the formula mentioned earlier:
R = (ρ x L) / A
R = (1.5 x 10^-6 Ω-m x 1 m) / (7.85 x 10^-6 m^2)
R = 1.5 x 10^-6 Ω / 7.85 x 10^-6 m
R = 0.19 Ω/m
Therefore, the resistance per unit length of the given nichrome wire is 0.19 Ω/m.
To find the resistance per unit length of the nichrome wire, we can use the formula:
R = (ρ * L) / A
where:
R is the resistance,
ρ (rho) is the resistivity,
L is the length of the wire, and
A is the cross-sectional area of the wire.
In this case, we are provided with the radius of the wire, not the diameter. So, we need to calculate the diameter first and then convert it to meters.
The diameter (d) of the wire can be calculated by multiplying the radius (r) by 2.
d = 2 * r
= 2 * 0.50 mm
= 1.00 mm
Next, we convert the diameter from millimeters to meters:
1 mm = 1 x 10^-3 meters
So, the diameter in meters (D) is:
D = 1.00 mm * 1 x 10^-3 m/mm
= 1.00 x 10^-3 m
Now, we can calculate the cross-sectional area (A) of the wire using the formula:
A = π * (D/2)^2
where π (pi) is a constant value of approximately 3.14159.
A = 3.14159 * ((1.00 x 10^-3 m)/2)^2
= 3.14159 * (5.00 x 10^-4 m)^2
= 3.14159 * 2.50 x 10^-7 m^2
= 7.85475 x 10^-7 m^2
Finally, we can substitute the given values into the formula for resistance per unit length to find R:
R = (ρ * L) / A
= (1.5 x 10^-6 W-m * L) / (7.85475 x 10^-7 m^2)
The unit of resistance per unit length is Ω/m (ohms per meter).