The heating element of a simple heater consists of a 2.2m--long, 0.70mm--diameter nichrome wire. When plugged into a 120 V outlet, the heater draws 7.5 A of current when hot.
I found that the wire's resistance when it was hot was 16 ohms. Now using this answer of 16 ohms calculate the resistivity of nichrome in this situation in units of ohms * m.
I can not get the answer. I have been using the formula R=pL/A which I rearranged to p=RA/L.
I got A by A=pie(7*10^-4)^2, which equals 1.54*10^-6.
I plugged in the numbers p=(16)(1.54*10^-6)/(2.2m) and got the answer 1.12*10^-5 but this isn't the right answer. I can not figure out what I did wrong. I would appreciate any help that gets me to the right answer! Thank you!!
You need to divide the diameter by two because the equation requires the radius not the diameter.
Well, it seems like you're getting quite the "resistance" while trying to calculate the resistivity! Let me try to bring some humor into the equation and guide you through this.
First, you've correctly rearranged the formula to solve for resistivity (p). However, your calculation for cross-sectional area (A) seems to be a bit off. You used the formula for the area of a circle, but you squared the diameter instead of the radius.
Let's give it another shot, shall we? The diameter of the wire is given as 0.70 mm, so the radius (r) would be half of that, which is 0.35 mm or 0.35 x 10^-3 m. Now we'll calculate A using the correct radius:
A = π × (0.35 x 10^-3 m)^2
Don't forget to square the radius, because squares are all the "buzz" these days!
Now, let's plug in the values:
A = π × (0.35 x 10^-3 m)^2
After evaluating this, we find that A is about 3.85 x 10^-7 m^2.
Now, you can plug this value back into your formula:
p = (16 Ω) × (3.85 x 10^-7 m^2) / (2.2 m)
Now, let's calculate:
p = 1.40 x 10^-7 Ω·m
And there you have it! The resistivity of the nichrome wire in this situation is approximately 1.40 x 10^-7 ohms·meter.
Remember, in the wonderful world of calculations, sometimes it just takes a bit of trial and error to find the right "resis-tance"! Hope this helps, and keep up the good work!
To determine the resistivity of nichrome, you need to use the formula correctly. The formula for resistance (R) is R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area.
In your calculation, you correctly rearranged the formula to solve for resistivity, ρ = RA/L. However, there was a mistake in calculating the cross-sectional area.
The correct calculation for the cross-sectional area is:
A = π(0.70 mm / 2)^2 = 0.385 mm^2 = 3.85 × 10^-7 m^2
Now, you can plug in the values into the equation:
ρ = (16 Ω) × (3.85 × 10^-7 m^2) / (2.2 m)
= 2.792 × 10^-6 Ω·m
Therefore, the resistivity of nichrome in this situation is approximately 2.792 × 10^-6 Ω·m.
To calculate the resistivity of the nichrome wire, you need to rearrange the equation correctly and ensure that all units are consistent. Here's the correct approach:
1. Start with the formula: R = p * (L / A), where:
- R is the resistance (given as 16 ohms),
- p is the resistivity (the value you want to find),
- L is the length of the wire (2.2 m), and
- A is the cross-sectional area of the wire.
2. Calculate the cross-sectional area (A):
- Given that the diameter of the wire is 0.70 mm, the radius (r) is half of that (0.35 mm or 0.35 * 10^(-3) m).
- Use the formula for the area of a circle: A = π * r^2.
- Substitute the values: A = π * (0.35 * 10^(-3))^2.
Note: Make sure to use the correct value of pi (approximately 3.14159265359).
3. Calculate the resistivity (p):
- Rearrange the formula: p = R * (A / L).
- Substitute the known values: p = 16 ohms * [(π * (0.35 * 10^(-3))^2) / 2.2 m].
4. Perform the calculations, making sure to use appropriate units:
- Evaluate the expression within brackets using the correct order of operations.
- Multiply the result by 16 ohms and divide by 2.2 m.
- Use a calculator to obtain the final answer.
By following these steps correctly, you should arrive at the correct value for the resistivity of nichrome in ohms * m.