Lab Report 2 - Lab Assignment 2 (Suzanne Bushnell) PDF

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Lab Assignment 2 (Suzanne Bushnell)...

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2. FACTORS AFFECTING RESISTANCE PHYS 206 Professor: Suzanne Bushnell September 18, 2021

Kendralyn Lavergne

I.

Length Dependence (Part 1) A. Predictions The resistance of a wire would increase as the length increases. Therefore, the relationship between resistance and length would be linear because x variable will increase as the y variable increases. B. Data and Graphs Table 1. Length and Resistance of aluminum wire (Radius: 1mm or 0.001m – Cross-Sectional Area: 3.14 x 10-6) Length (m) 1.5 8.0 6.3 2.7 2.0 3.1 6.9 7.3 0.8 6.4

Resistance (ohm) 14.16 x 10-3 73.47 x 10-3 57.66 x 10-3 25.20 x 10-3 18.48 x 10-3 28.51 x 10-3 63.73 x 10-3 67.40 x 10-3 7.26 x 10-3 58.76 x 10-3

Resistance as a function of length on aluminum wire

Fig 1. Resistance as a function of length on a gold wire Table 2. Length and resistance of copper wire (Radius: 1mm or 0.001m , Cross-sectional area: 3.14 x 10-6 Length (m) 6.4 2.2 3.5 5.5 4.8 3.1 2.0 4.0 5.1 1.5

Resistance (ohm) 36.12 x 10-3 12.11 x 10-3 19.29 x 10-3 30.85 x 10-3 26.98 x 10-3 17.22 x 10-3 11.22 x 10-3 22.66 x 10-3 28.66 x 10-3 8.64 x 10-3

Resistance as a function of length (Copper)

Fig 2. This graph shows resistance as a function of length of a copper wire. C. Analysis My experiment revealed that as the length increased, the resistance of the wire also increased. Therefore, it was shown as a linear relation on the graph forming a straight positive line with a positive slope. My prediction was proven correct because the relationship showed a linear relation revealing that as the resistance variable increased, so did the length variable. The theory equation is R = pL/ A where R is the resistance, p is resistivity of the metal of the wire, L is the length of the wire and A is the cross-sectional area of the wire. My graph demonstrates the theory equation because the relationship between resistance and length is a linear relation, as shown in the graphs. The slope represents the resistance for that specific length of wire (p=R/L). Resistivity Calculations: 3.14 x (0.001m)2 = 3.14 x 10-6 Aluminum: 3.14 x 10-6 m (9.18 x 10-3Ω m) = 2.88252 x 10-8Ω m Copper: 3.14 x 10-6 (5.64 x 10-3) = 1.77096 x 10-8Ω m Percent Error Calculations: Aluminum: (2.82 x 10-8Ω m) – (2.88252 x 10-8Ω m) = -6.252 x 10-10Ω m -6.252 x 10-10Ω m / 2.82 x 10-8 Ω m = |-0.0221702128| x 100 = 2.21%

Copper: (1.72 x 10-8Ω m) – (1.77096 x 10-8Ωm) = -5.096 x 10-10Ω m (-5.096 x 10-10 Ω m) / (1.72 x 10-8Ωm) = |-0.029627907| x 100 = 2.96% Some errors I made while calculating the percent error were using the wrong block size for the wire several times. I did not make my circle the biggest it could go for the experiment, and it caused my percent error to increase significantly. Another error I made during this experiment was not using the correct units for the resistance on the capstone graph. This caused my error to skyrocket into the thousands.

Part 2: Diameter (gauge) dependence A. Predictions The relationship between resistance and radius will be linear because both x and y variables will increase or decrease together. The cross-sectional area is a circle, therefor B. Data and Graphs Table 3. Radius vs Resistance Radius (m) 0.001 0.0007 0.0001 0.0008 0.0009 0.0002 0.0004 0.0003 0.0005 0.0006

Resistance (ohm) 5.99 11.50 584.42 9.27 7.18 127.61 33.77 57.79 23.56 16.40

Fig 3. Graph of resistance as a function of radius with graphite C. Analysis My results disagree with my prediction because I predicted that the relationship between radius and resistance would be linear. The variables do not increase or decrease together to form a linear equation. Instead, this graph represents an inverse equation meaning that as one variable increases, the other will decrease as shown above in the graph. The equation for the graph in this experiment is 0.0183 / (x-6.96x10-5) + (-17.3). The theory equation is R = pL/A where L is length, A is the cross-sectional area, p is the resistivity and R is resistance. My equation is similar to the theory equation because it uses length variables and resistance variables....