Lab_2_Report_ECEN_214_506.docx

ECEN-214 - Lab Report Lab Number: 2 Lab Title: Non-Ideal Sources Section Number: 506 Student Names: Sterling Light, Rushi Penki TA Name: Nicholas Jeon Date measurements performed: 9 February 2024 Date report due: 22 February 2024

Procedure: The group first connected an AA battery to two different nodes on the provided breadboard. Following this, a parallel resistor combination with an equivalent resistance of close to 50 Ohms was added across the terminals of the battery. Both the actual resistance of this combination and the voltage across it were measured and recorded. This process was repeated an additional six times, using resistors and resistor combinations with resistances equivalent to 100Ω, 200Ω, 1000Ω, 1100Ω, 1500Ω, and 2000Ω. After this, the AA battery was swapped out for another AA battery, and the entire process depicted in the first paragraph was repeated. The original AA battery was then added back into the circuit along with the second one, forming a new equivalent source with a voltage value of approximately 3V. The entire process depicted in the first paragraph was then repeated. Data Tables: The relevant data table from Task #1 is included below. Nominal R L , Measured R L , and Measured V L for the First AA Battery Nominal RL (Ohms) Measured RL (Ohms) Measured VL (Volts) 50Ω 49.8Ω 1.636V 100Ω 99.1Ω 1.651V 200Ω 198Ω 1.66V 1000Ω 987Ω 1.668V 1100Ω 1085Ω 1.668V 1500Ω 1481Ω 1.669V 2000Ω 1973Ω 1.669V The relevant data tables from Task #2 are included below. Nominal R L , Measured R L , and Measured V L for the Second AA Battery Nominal RL (Ohms) Measured RL (Ohms) Measured VL (Volts) 50Ω 49.6Ω 1.632V

100Ω 98.98Ω 1.654V 200Ω 197.87Ω 1.666V 1000Ω 986.6Ω 1.678V 1100Ω 1085.66Ω 1.678V 1500Ω 1481.64Ω 1.679V 2000Ω 1975.17Ω 1.679V Nominal R L , Measured R L , and Measured V L for the Two AA Batteries in Series Nominal RL (Ohms) Measured RL (Ohms) Measured VL (Volts) 50Ω 49.552Ω 3.174V 100Ω 98.8Ω 3.247V 200Ω 198.470Ω 3.298V 1000Ω 986.9Ω 3.331V 1100Ω 1084.97Ω 3.333V 1500Ω 1480.33Ω 3.334V 2000Ω 1974.88Ω 3.335V Data Plots: The plots found on the succeeding pages are all the relevant plots from the group’s analysis of the data gathered in Task #1.

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The linearized graph of voltage across the load derived from Equations 1 and 2 provided in the laboratory manual is provided below on the subsequent page.

The equation featured immediately below the title is the equation for the line of best fit. Using this data and the structure of Equation 2, it can be reasonably concluded that the source voltage V s = 1.67 V, and the internal resistance of the battery R s = 1.05 Ω . The battery’s manufacturer reports that the battery provides a voltage of 1.5 V, so the values derived here are reasonable estimates. That being said, the measured value V S from this graph is not 1.5 V, meaning that there is some error in our measurements. This matter is discussed further in the discussion section.

A similar set of graphs is included below for the second AA battery.

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From these graphs, it can be measured that for the second AA battery, V S = 1.68 V, and R S = 1.5 Ω. As with the previous trial, these values indicate that the group’s measurements were subject to a particular degree of error, which is explored in the discussion section. Appropriate graphs for the two batteries connected in series are included below.

From these graphs, the equivalent voltage of the two batteries in series is V S = 3.34 V, and the internal resistance R S is 2.65 Ω. The error in these measurements is touched upon in the discussion section. The group notes that the measured values follow the trends established in previous estimations; the curve of V L vs. V L R L is downward-sloping, and the measured value V S is slightly above the theoretical value. Sample Calculations: All of the calculations used in this laboratory are included below. First, these equations were used to create equivalent resistance values beyond the range provided by each individual resistor in the group’s parts kit. The following equation applies to resistors placed together in series: R eq = R 1 + R 2 The following equation applies to resistors placed together in parallel: R eq = 1 1 R 1 + 1 R 2 Another equation, featured below, was utilized in the graphing process. V L = V S − V L R L R S This equation was used in the V L vs. V L R L graph to plot the curve. Using the best-fit line on that graph, the group identified the values for V S and R S . Using this methodology, within the equation for the best-fit curve, R S was equivalent to the negative of the coefficient of x, and V S was equivalent to the measured intercept value.

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Lastly, the following equation was used to estimate the percentage error in the group’s calculations. %Error = V m − V p V p ∗ 100 In this equation, V m is the measured voltage of the source, and V p is the voltage provided by the manufacturer (the voltage value inscribed on the side of the battery or, in the case of the batteries in series, the sum of the inscribed values on the two batteries). Discussion: The questions asked in the laboratory manual that still need to be answered will be addressed below. In the laboratory manual, the group was instructed to ensure that a resistance of no less than 10 Ohms is applied across the terminals of the battery. This is to ensure that the equipment in the laboratory and parts kit are not damaged; a load resistance value less than 10 Ohms poses the threat of conducting an exceedingly high current, which in turn will lead to the resistor dissipating an exceedingly high amount of power. Every resistor has a power rating, which describes how much power a resistor can dissipate before sustaining damage. If the resistance is too low, the power dissipated can exceed this rating, which will damage the resistor. The graphs in the Data Plots section allowed the group to estimate the source voltage and internal resistance of the batteries utilized. The values determined were around the values expected from the voltage sources that were utilized, which indicates that the measurements taken during the laboratory were generally accurate. However, there was some error present; each battery individually provides 1.5 V, but the measured voltage provided by the first and second batteries were 1.67 V and 1.68 V, respectively. Furthermore, the equivalent voltage of the batteries in series should be 3 V, but the measured voltage is 3.34 V. This suggests that the

measurements taken in the laboratory were subject to a certain degree of error; for the first, second, and series batteries, the measured voltages were off by 11.3%, 12%, and 11.3%, respectively. Some sources of the errors described in the previous paragraph can be attributed to equipment; the AA batteries likely did not provide exactly 1.5 V, for instance. Beyond that, the resistors that the group used had actual resistance values that were not equivalent to the nominal resistance values. Since the nominal resistance values were used in the calculations for the data plots, the predicted V S and R S are going to be somewhat inaccurate. The best way to reduce the error in the measurements, therefore, would be to either adjust the actual load resistance values so that they are closer to the nominal values, or to alternatively make the calculations in the Data Tables section using the measured resistance values instead of the nominal ones. Miscellaneous: The signed page of the laboratory notebook is included below.

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