A wire is made of a material with a resistivity of 4.85109 × 10−8 Ω · m . It has length 5.57436 m and diameter 0.36396 mm .
What is the resistance of the wire?
Answer in units of Ω
R=ρL/A
A=πd²/4
Well, if it's not already obvious, this wire isn't interested in making things easy for us. So let's embrace the challenge and calculate its resistance!
To do that, we need to use the formula for electrical resistance, which is R = (ρ * L) / A, where ρ is the resistivity, L is the length of the wire, and A is the cross-sectional area.
First, let's convert the given diameter into meters. The diameter is 0.36396 mm, which is equal to 0.00036396 m. But since we're dealing with the radius, we divide this value by 2, giving us a radius (r) of 0.00018198 m.
Next, let's calculate the cross-sectional area (A) of the wire using the formula A = π * r^2. Plugging in the values, we get A = π * (0.00018198 m)^2.
Now we have all the information we need to calculate the resistance. Plugging in the values into the formula, we get R = (4.85109 × 10^(-8) Ω · m * 5.57436 m) / (π * (0.00018198 m)^2).
Doing the math, the resistance of this wire is approximately 2.9059 Ω. So there you have it, the resistance of this wire in all its quirky glory!
To find the resistance of the wire, we can use the formula:
Resistance = (resistivity * length) / cross-sectional area
First, let's calculate the cross-sectional area of the wire:
The diameter of the wire is given as 0.36396 mm.
The radius of the wire is half of the diameter, so the radius is 0.36396 mm / 2 = 0.18198 mm.
To convert mm to meters, we divide by 1000:
Radius = 0.18198 mm / 1000 = 0.00018198 m.
The formula for the area of a circle is:
Area = π * radius^2
Plugging in the values:
Area = π * (0.00018198 m)^2 = π * 3.3071e-8 m^2
Now, we can calculate the resistance:
Resistance = (4.85109 × 10^-8 Ω · m) * (5.57436 m) / (π * 3.3071e-8 m^2)
Resistance = 0.000258 Ω (rounded to 3 decimal places)
Therefore, the resistance of the wire is approximately 0.000258 Ω.
To find the resistance of the wire, we can use the formula:
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
First, we need to calculate the cross-sectional area of the wire:
A = π * r^2
where r is the radius of the wire.
The given diameter is 0.36396 mm. We need to convert this to meters:
d = 0.36396 mm / 1000 = 0.00036396 m
Next, we can calculate the radius:
r = d / 2 = 0.00036396 m / 2 = 0.00018198 m
Now we can calculate the cross-sectional area:
A = π * (0.00018198 m)^2 = 1.04378 × 10^-7 m^2
Finally, we can substitute the values into the resistance formula:
R = (4.85109 × 10^-8 Ω · m * 5.57436 m) / (1.04378 × 10^-7 m^2)
R = 2.59578 Ω
Therefore, the resistance of the wire is approximately 2.59578 Ω.