A wire is made of a material with a resistivity
of 2.08184 × 10−8 Ω · m . It has length 4.42917 m and diameter 0.6763 mm .
What is the resistance of the wire?
Answer in units of Ω.
Would you just use the equation R = PL /a?
yup
To calculate the resistance of the wire, you need to use the formula for resistance:
R = ρ * (L / A),
where:
R = resistance,
ρ (rho) = resistivity of the material,
L = length of the wire,
A = cross-sectional area of the wire.
In this case, the resistivity (ρ) is given as 2.08184 × 10^(-8) Ω·m. The length (L) is given as 4.42917 m.
To find the cross-sectional area (A), we need to use the diameter (d). However, the diameter is given in millimeters, so we need to convert it to meters by dividing it by 1000:
d = 0.6763 mm = (0.6763/1000) m.
Next, we need to use the formula for the area of a circle:
A = π * (d/2)^2,
where π (pi) is a constant approximately equal to 3.14159.
Now we can plug these values into the resistance formula:
R = (2.08184 × 10^(-8) Ω·m) * (4.42917 m) / (3.14159 * (0.6763/2000 m)^2).
Calculating this expression will give you the resistance of the wire in ohms (Ω).