A uniform wire of diameter 0.3 mm gives (length in m, measured resistance in Ω) readings (0.2, 1.2), (0.4, 2), (0.6, 2.8), (0.8, 3.6), (1, 4.4). Model the reading as Rmeasured = ρL/A + Rc, where Rc is constant contact resistance and A = πd²/4. (a) Determine ρ and Rc. (b) Explain why using one reading as ρ = RA/L is biased. (c) State two practical controls.

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Accepted Answer

Resistivity 2.827e-7 Ω m; contact resistance 0.4 Ω; a one-point calculation overestimates resistivity. The slope of resistance against length is ΔR/ΔL = 4 Ω/m. Under the supplied model this equals ρ/A, while the vertical intercept is the constant contact resistance Rc = 0.4 Ω. Convert the diameter to 0.0003 m and calculate A = πd²/4 = 7.069e-8 m². Hence ρ = slope × A = 2.827e-7 Ω m. A single resistance includes the positive contact term as well as the wire resistance. Substituting it directly into RA/L attributes the contact resistance to the wire, systematically overestimating resistivity; the graph gradient excludes a constant offset. Use a small current and switch off between readings to limit temperature changes, which alter resistivity. Measure diameter at several positions and orientations, checking the micrometer zero. Keep the contacts consistent so the assumed constant contact resistance remains a reasonable model.

Wire resistance with contact resistance 1

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Resistance versus wire length

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Resistance versus wire length — supplied values
Length / m	Resistance / Ω
0.2	1.2
0.4	2
0.6	2.8
0.8	3.6
1	4.4