Mitchell,J.L. |1
Ohm’s Law and Resistivity Lab Questions and Results
Introduction: Direct constant (DC) circuits were built using DC power supplies and resistors in order to investigate the properties of resistance (R). Resistance is the measure of difficulty regarding current flow through a circuit wire and is determined by type of material (resistivity), the cross sectional area of the given material as well as the length. In part A of the Ohm’s Law and Resistivity lab, the Rheostat was used to examine resistive load (R) under varying conditions of both current and voltage. In part B of the procedure, the tap was moved in 20-95% intervals of distance on along the Rheostat under a constant voltage, so as to explore the effects of altering current on the resistant properties of the device. The experimental resistance was obtained using a multimeter and a theoretical resistance was calculated using Ohm’s Law. The current of a conductor between two points demonstrates a voltage directly proportional to the current and inversely proportional to the resistance, and is defined by Ohm’s Law; V=IR. In part C of the experiment, voltage and current were measured in copper wire coil of varying diameters and length. This was done in order to determine if differences attributed to length or area would contribute to a change in resistance.
Questions: Part A; Part B
It is not possible to calculate approximate uncertainty of the resistance in an Ohmic device. In a device known to be “Ohmic,” 1 Ω = 1 V/A, and resistance is found to be independent (a constant) and unchanged by both voltage and current. The experimental differences were nominal when comparing our experimental and theoretical values in both Part A and Part B. Both systemic errors derived from defects in the electronic equipment used, as well as random error (such as room temperature), most likely contributed to the differences in these values. If no errors were made in the experiment, both the theoretical and calculated resistivity values should have been the same. This is because voltage and current do not have an effect on the resistance value found in an Ohmic device. However, R=ρ(L/A) therefore, resistance is directly affected by the resistivity unique to a material, as well any changes in length or area.
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Table I. shows that a linear relationship found in voltage versus current, with a slope of resistance R/1 defined by the values V/I. This provides evidence that the Rheostat can be characterized as an Ohmic device. Additionally, Table II. also reveals that a linear relationship is found in current versa voltage. Conversely, 1/R is the slope of resistance defined by I/V.
Table 1. The slope of resistance (R/1) as determined by
y=0.0115x-0.0037
Table 2. The slope of resistance (1/R) as determined from y=87.05x+0.3446, on the bas
Questions: Part C; Part D •
The 2:1 ratio of the lengths 20m and 10m, were equal to the ratios of their resistances which were also approximately 2:1. This indicates that doubling the length in a wire will result in a resistance that is also doubled. The 2:1 ratios of the radii 0.000318m and 0.000152 differed from the ratios of their resistances and were found to be approximately 0.22:1. It is evident that as direct correlation exists between the length of a wire and/or the radii thereof, that determines resistance. Therefore, a shorter wire with a wider diameter demonstrates significantly less resistance as compared to a wire possessing a greater length with a diameter that is less wide; doubling the cross-sectional area will halve the resistance. Evidence for this is provided by the calculations arranged below.
Calculations for Same Radii (m)-Different Length (m) Ratios of Resistance (Ω): Radius (0.000318) Length (10)
Mitchell,J.L. |3 Resistance (0.4452640; 0.427) Radius (0.000318) Length (20) Resistance (0.885789; 0.857143; 7.19474; 7.74359) Radius (0.000152) Length (10) Resistance (1.98421; 1.98298) Radius (0.000152) Length (20) Resistance (3.78947; 4.0) Ratio for Lengths (20/10)=2:1 Ratio of Resistances≈2.0: 1.0 0.885789/.4452640=1.99/1 0.885789/0.427=2.07/1 0.857143/0.4452640=1.93/1 0.857143/0.427=2.01/1 3.78947/1.98421=1.91/1 3.78947/1.98298=1.91/1 4.0/1.98421=2.02/1 4.0/1.98298=2.01/1
Calculations for Same Length (m)-Different Radii (m) Ratios of Resistance (Ω):
Length (10) Radius (0.000318) Resistance (0.445263; 0.427) Length (10) Radius (0.000152) Resistance (1.98421; 1.98298; 7.19474; 7.74359) Length (20) Radius (0.000318) Resistance (0.885789; 0.857143) Length (20) Radius (0.000152) Resistance (3.78947; 4.0)
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Ratio for Radii (0.000318/0.000152)≈2:1 Ratio for Resistances≈0.22:1 0.445263/1.98421=.22/1 0.445263/1.98298=.22/1 0.427/1.98421=.22/1 0.427/1.98928=.21/1 0.885798/3.8974=.23/1 0.885798/4.0=.22/1 0.857143/4.0=.21/1
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