If 49 m of nichrome wire is to have a resistance of 13.0 ohms at 20°C, what diameter wire should be used?
I've done this:
(108e-8)(49)/10.0 ohms = 5.29e-6m^2
Then 5.29e-6m^2/pi
then r = sqrt(1.68e-6m^2)
and got .00129 = 1.29e-3
1.29mm
r=2(1.29mm) = 2.58mm
But this is wrong. Any suggestions?
Where did the 13 ohms go?
Ooo. Gosh, I must have just been looking at the wrong number or something. I feel silly now.
2.27mm is the new answer I got, which is correct. Thanks for pointing that out, Bob. I was going insane trying to figure this out.
To find the correct diameter of the wire, we can use the formula for resistance of a wire:
R = ρ * (L / A)
where R is the resistance, ρ (rho) is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
In this case, we are given the resistance (R = 13.0 ohms) and the length (L = 49 m). We need to find the cross-sectional area (A) in order to determine the diameter.
The formula for the cross-sectional area of a wire is:
A = π * (d/2)^2
where d is the diameter of the wire.
To find the correct diameter, we can rearrange the formula for resistance and substitute in the given values:
R = ρ * (L / A)
Solving for A:
A = ρ * (L / R)
Now, let's calculate A using the given values:
A = (108e-8 ohm*m) * (49 m / 13.0 ohms)
A = 4.078154e-5 m^2
Next, we can calculate the diameter (d) by rearranging the formula for the cross-sectional area:
A = π * (d/2)^2
Solving for d:
d/2 = sqrt(A / π)
d = 2 * sqrt(A / π)
Now, let's substitute the calculated value of A into the formula:
d = 2 * sqrt(4.078154e-5 m^2 / π)
d = 0.010195 m (approximately)
To convert the diameter from meters to millimeters, multiply by 1000:
d = 10.195 mm (approximately)
Therefore, the correct diameter of the wire to be used is approximately 10.195 mm.