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

VARIABLES:

Independent Variables:

1. Length of the wire used. (l)

Dependent Variables:

1. Resistance of the circuit. (Ω)

Controlled Variables:

1. Voltage of the circuit. (V) – The same power source was used for all trials of the experiment.
2. Texture of the Nichrome wire. – It was wiped clean of any contaminants such as oxides etc.
3. The measuring tape – The same measuring tape was used to measure all heights.

PROCEDURE:

A simple circuit was set up with the Nichrome wire as the resistor. For different sets of data, the length of the Nichrome wire was altered by making only a fraction of the full wire part of the circuit. A ruler was used to measure the length of the wire part that was part of the circuit and an ohmmeter was used to identify the resistance of the circuit. Five trials were taken for five different lengths to obtain a reliable, wide range of data.

Safety Precautions:

1. Precaution was taken so that the Nichrome wire would not hurt the finger.
2. Precaution was taken to make sure there were no fire hazards due to short-circuit.
3. Precaution was taken to make sure that no injury was caused because of electrocution due to careless behavior.

RAW DATA COLLECTION:

The resistance of the circuit for different lengths were collected as raw data and are tabulated below:

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 = ±0.1Ω.

Using a spreadsheet, the average time taken was calculated and is displayed in the table below:

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 = ±0.15Ω. 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. This, uncertainty can be any.

To calculate d, l is to be plotted on the y-axis against R on the x-axis. Using the ‘scatter plot’ function, the following graph was drawn:

Uncertainty in the gradient of the slope:

.

Therefore, average gradient = 0.1744 ± 3.2% = 0.1744 ± 0.006

To calculate the diameter of the Nichrome wire:  

 

•  m

Therefore, using the ‘resistivity’ method, the diameter of the Nichrome wire is identified to be 0.053 ± 0.001cm.

CONCLUSION AND EVALUATION:

As it can be seen from the total uncertainty calculation, the experimentally deduced value of the diameter of the Nichrome wire was accurate to a large extent. In fact, the literature value provided by the manufacturer… The difference…

The r2 value for the line of best is 0.9956 which shows excellent linear correlation between the resistance and the length of a conductor, confirming the equation However, the minor noticeable distance between the average slope and the minimum and maximum slopes is due to the increasing uncertainty in the measurement of the length.

The uncertainty, however small, cannot be ignored and they must be explored so that if possible, they can be avoided in the future. Firstly, the recording of the length of the Nichrome wire was no so accurate because of the uncertainty in the ruler and its inability to measure all the lengths at one go. A longer ruler or a measuring tape could be used to avoid these kind of easily avoidable errors. Another problem was that the wire was often crooked at some places and straightening it could have caused it to crack so they were not completely straightened. In fact, the wires were looped around several bobs and the distance between the bobs were measured to give an accurate estimate of the length of the wire. Another issue that arose due to the usage of the bobs was that it was difficult to measure the length of the wire that was used to complete the loop around the bob. 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 Ω.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.

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