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Homework Statement
We were given five samples of nichrome wire, each with a different diameter but the same length. A micrometer was used to measure the diameters. We then measured and recorded the electrical resistance, R in Ohms of each nichrome sample with a DMM. I will try to summarize all of this as clearly as possible below:
Sample #, Diameter (± 0.01 mm), Resistance
20, 0.80 mm, 23.6 ohms
22, 0.62 mm, 36.5 ohms
24, 0.56 mm, 57.4 ohms
28, 0.31 mm, 159.0 ohms
30, 0.26 mm, 226.8 ohms
Length of wire: 10.00 ± 0.01 mWe are required to plot a graph of resistance, R (in Ohms) versus the inverse square of the diameter (in m^-2), i.e.; "R" vs. 1/d^2. We then have to calculate the slope of the graph, and from the slope determine the resistivity p of nichrome wire. We then compare our value of p with the published value of p = 1.18 x 10^-6 ohm*m.
Homework Equations
The electrical resistance R (Ohm) of a particular cylindrical sample of material is related to the resistivity by:
R = pL/A = 4pL/pi^2 = (4pL/pi)(1/d^2)
R = 1/d^2
where L is the length of the wire, A = (pi*d^2)4 is the cross-sectional area, p is the resistivity, and d is the diameter of the wire.
The Attempt at a Solution
My problem lies in calculating the inverse squared diameter itself, and plotting the values. My first instinct was to convert the diameters to m, so instead of 0.80 mm we have 0.80 x 10^-3 m. I then square the value, then invert it to get 1562500 m^-2. HOW does this make any sense? It also looks off when i try to graph the values on excel; with 1/d^2 on the x-axis and R on the y-axis, the slope should be 4pL/pi, right? I've written out all of the equations relevant to this lab right out of the lab manual -- so why are the 1/d^2 values so large? Did I miss something, what could I be doing wrong?
Any help would be immensely appreciated!