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Determining the diameter of a piece of Nichrome wire by determining its resistivity

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Introduction

Candidate Name: Session: May 2015 Page | International Baccalaureate Diploma Program (IBDP) Session: May 2015 Physics HL Lab Report Lab Report Title: Determining diameter using resistivity. Criteria Assessed: * Data Collection and Processing (DCP) * Conclusion and Evaluation (CE) Candidate Name: Candidate Number: International School, Singapore AIM: To determining the diameter of a piece of Nichrome wire by determining its resistivity. INTRODUCTION: Metals have low resistance due to their delocalized field of electrons. However, different metals have different values of resistance. In this experiment, the students were given a spool of Nichrome wire to determine its diameter. Nichrome, as the name suggests, is an alloy of Nickel, Chromium and Iron. The resistance of a conductor depends on its inherent resistivity (ρ), length (l) and its cross-sectional area (A). The resistance is given by the following formula (#1): . Where, R = Resistance (â¦) ρ = Resistivity (â¦.m) l = length (m) and, A = cross-sectional area of the conductor. To determine the cross-sectional area of the wire, the diameter was first determined using a micrometer screw gauge. The formula (#2) that relates the diameter to the cross sectional area of the wire is: The electrical resistance can be determined by an ohmmeterlength, using a ruler, and the resistivity was determined by the literature value of 1.25×10-6 â¦.m.[1] Substituting the literature value for Nichrome’s resistivity () ...read more.

Middle

± 0.4 8.8 8.8 8.7 8.5 8.6 5 187.5 ± 0.5 10.6 10.5 10.6 10.4 10.6 Table 1: Raw Data: Total electrical resistance of the circuit for each length of the resistor. Uncertainties: * Uncertainty in the length l = Uncertainty of ruler (± 0.1cm) × Number of times, it was used. * Sample calculation for 2nd of data (l = 75.6cm): (38.3 ± 0.1cm) + (38.3 ± 0.1cm) = 75.6 ± 0.2cm * Uncertainty in R = Uncertainty in instrument = ±0.1â¦. Using a spreadsheet, the average time taken was calculated and is displayed in the table below: Serial No. Length (m) Resistance / R (â¦) Average 1 0.383 ± 0.001 2.56 ± 0.15 2 0.756 ± 0.002 4.48 ± 0.15 3 1.129 ± 0.003 6.48 ± 0.20 4 1.502 ± 0.004 8.68 ± 0.15 5 1.875 ± 0.5 10.54 ± 0.10 Table 2: Processed Data: Average resistance for each length of the Nichrome wire. Uncertainties: * Uncertainty in Resistance / R = Random Error = * Sample calculation for 1st set of data (l = 0.383m): Therefore, Uncertainty = ±0.15â¦. Note: The higher of the random error and the instrumental error is taken. In case of the 5th set of data, random error = instrumental error. ...read more.

Conclusion

A possible workaround both these problems can be to use a thread to run along the Nichrome wire and then measure the thread to determine the length of the Nichrome wire used. Another limitation to the procedure of the experiment is the assumption of the electrical resistivity of the Nichrome wire. The actual range is 1.00 to 1.50 (×10-6 â¦.m) but the median, 1.25 was assumed. There is no possible way to tell the exact electrical resistivity without knowing the exact composition of the wire and this is because resistivity is a property that is specific to the composition of the conductor and slight changes in the composition can produce significant changes in the value for the resistivity of the conductor. Depending on the manufacturer’s label for the diameter is accurate but often these values are rounded off to suit the gauge number of the wire. For example, if a 2AWG wire requires a 10mm diameter, most manufacturers will label even a 9.8mm to be 10mm because of their own economic benefits. Therefore, the most accurate way would be use a micrometer screw gauge to measure the diameter of the wire at different locations and then match the experimental value obtained from this experiment against the average of the micrometer readings. This way, dependence on secondary data is minimized and a higher level of confidence can be displayed in the readings. ________________ [1] http://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html, Accessed on 30/01/2015 ...read more.

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