A 19 m long piece of wire of density 8.34 g/m3
has a diameter of 12.593 mm. The resistiv-
ity of the wire is 1.7e-8(ohm)(m) at 20 degrees celsius.
The temperature coefficient for the wire is
0.0038(degrees celsius)^-1.
Calculate the resistance of the wire at 20degrees Celsius.
Answer in units of .
(part 2 of 2) 10 points
Calculate the difference in the resistance of
the wire between 35degrees Celsius and 68degrees Celsius.
Answer in units of .
hi im the one who posted this question, i just wana say that the units of the answer in part 2 should be in ohms.
To calculate the resistance of the wire at 20 degrees Celsius, we can use the formula for resistance:
Resistance (R) = resistivity (ρ) * length (L) / cross-sectional area (A)
We first need to calculate the cross-sectional area of the wire. The diameter (d) is given as 12.593 mm, so we can calculate the radius (r) using the formula:
Radius (r) = diameter (d) / 2
Next, we can calculate the cross-sectional area (A) using the formula for the area of a circle:
Area (A) = π * radius^2
Now, we can substitute the given values into the formula to find the resistance:
Resistance (R) = resistivity (ρ) * length (L) / cross-sectional area (A)
Once we have the resistance at 20 degrees Celsius, we can calculate the difference in resistance between 35 degrees Celsius and 68 degrees Celsius using the temperature coefficient. The formula for the change in resistance with temperature is:
Change in resistance (ΔR) = resistance (R) * temperature coefficient (α) * (new temperature - reference temperature)
Let's plug in the given values and calculate:
Given:
ρ = 1.7e-8 (ohm)(m)
L = 19 m
d = 12.593 mm
α = 0.0038 (degrees Celsius)^-1
Reference temperature = 20 degrees Celsius
New temperature 1 = 35 degrees Celsius
New temperature 2 = 68 degrees Celsius
Step 1: Calculate the resistance at 20 degrees Celsius
- Calculate the radius:
r = d / 2 = 12.593 mm / 2 = 6.2965 mm
- Convert the radius to meters:
r = 6.2965 mm * 1 m / 1000 mm = 0.0062965 m
- Calculate the cross-sectional area:
A = π * r^2 = 3.1416 * (0.0062965 m)^2 = 7.8504e-5 m^2
- Calculate the resistance:
R = ρ * L / A = (1.7e-8 (ohm)(m)) * (19 m) / (7.8504e-5 m^2) = 4.1328 ohms
The resistance of the wire at 20 degrees Celsius is 4.1328 ohms.
Step 2: Calculate the difference in resistance between 35 degrees Celsius and 68 degrees Celsius
- Calculate the change in resistance for temperature 1 (35 degrees Celsius):
ΔR1 = R * α * (new temperature 1 - reference temperature) = 4.1328 ohms * 0.0038 (degrees Celsius)^-1 * (35 - 20) degrees Celsius = 0.2997 ohms
- Calculate the change in resistance for temperature 2 (68 degrees Celsius):
ΔR2 = R * α * (new temperature 2 - reference temperature) = 4.1328 ohms * 0.0038 (degrees Celsius)^-1 * (68 - 20) degrees Celsius = 0.9109 ohms
The difference in resistance for the wire between 35 degrees Celsius and 68 degrees Celsius is 0.9109 ohms.