Lab 3 report

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Community College of Philadelphia *

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Electrical Engineering

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Jan 9, 2024

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COMMUNITY COLLEGE OF PHILADELPHIA PHIALDELPHIA, PENNSYLVANIA Experiment Number: 3 Title: Parallel and Series Circuits Performed by: Partners: N/A Engineer Course: Engineering 102 Lab Section No: 901 Lab Day/Hour: Tue Thu 1PM-3PM Lab Instructor: Dr.W.A.Gontar Date Performed: 09/28/2021 Date Due: 10/05/2021

Purpose The purpose of this experiment is to be able to draw a graph of I versus V from the voltage and current values of resistors in series connection and parallel connection by using the Data Acquisition Unit and the Triple Output Power Supply. Procedures First, remember to check which channel the equipment would operate on to adjust accordingly. Three given resistors were measured by using the Data Acquisition Unit, and then their values were recorded. In series connection, the circuit was set up as shown in Figure 1. Increasing the Triple Output Power Supply from 1 to 5 volts to measure the voltage across each resistor, and the voltage values were displayed on the screen of the Data Acquisition Unit. After the voltage values of the three resistors were recorded, switch to channel 21 or 22 of the Data Acquisition Unit and adjust the wire of the circuit to measure the current values with the same steps as measuring the voltage. The current values were recorded. In parallel connection, the circuit was set up as shown in Figure 2. The measurement steps were also increasing from 1 to 5 volts to measure the current through each resistor (remember use channel 21 or 22 to measure the current), and then the values were recorded. After that, switch to channel applied to the Data Acquisition Unit and adjust the wire of the circuit to measure the voltage across each resistor with the same steps as measuring the current. The voltage values were recorded. The measured values were compared with the values calculated by the formula through the percent difference. Three graphs were drawn to represent the relationship between voltage (V) and current (I) for each resistor. The detailed procedure that was followed can be found in Physics Laboratory Instructions, Volume I, Community College of Philadelphia, John Wiley & Sons, 2005. Data sheets

Part I – Value of Resistors Resistor Color Code Nominal Value ± Tolerance Measured Value 1 Brown-Black-Red-Gold 1000 ± 50 0.985 kΩ = 985 Ω 2 Red-Red-Red-Gold 2200 ± 110 2.171 kΩ = 2171 Ω 3 Orange-Orange-Red-Gold 3300 ± 165 3.271 kΩ = 3271 Ω Part II – Voltage and Current Values of Resistors Measuring by the Equipment ► The series circuit Voltage [V] Current for the whole circuit [A] 1 0.159 x 10 -3 2 0.315 x 10 -3 3 0.470 x 10 -3 4 0.625 x 10 -3 5 0.781 x 10 -3  Resistor 1 Voltage [V] Voltage across [V] 1 0.157 2 0.310 3 0.464 4 0.617 5 0.770  Resistor 2 Voltage [V] Voltage across [V] 1 0.347 2 0.685 3 1.022 4 1.360 5 1.698  Resistor 3 Voltage [V] Voltage across [V] 1 0.522 2 1.032 3 1.541 4 2.050 5 2.559 ► The parallel circuit

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Voltage [V] Voltage for the whole circuit [V] 1 1.021 2 2.020 3 3.014 4 4.01 5 5.01  Resistor 1 Voltage [V] Current [A] 1 1.036 x 10 -3 2 2.044 x 10 -3 3 3.057 x 10 -3 4 4.068 x 10 -3 5 5.080 x 10 -3  Resistor 2 Voltage [V] Current [A] 1 0.471 x 10 -3 2 0.930 x 10 -3 3 1.389 x 10 -3 4 1.849 x 10 -3 5 2.308 x 10 -3  Resistor 3 Voltage [V] Current [A] 1 0.313 x 10 -3 2 0.618 x 10 -3 3 0.923 x 10 -3 4 1.228 x 10 -3 5 1.534 x 10 -3

Graphs and Diagrams ► In series connection 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Graph of Voltage vs Current for Resistor 1 Voltage across [V] Current [mA] 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Graph of Voltage vs Current for Resistor 2 Voltage across [V] Current [mA] 0 0.5 1 1.5 2 2.5 3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Graph of Voltage vs Current of Resistor 3 Voltage across [V] Current [mA]

► In parallel connection 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 1 2 3 4 5 6 Graph of Voltage vs Current for Resistor 1 Voltage across [V] Current [mA] 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 0.5 1 1.5 2 2.5 Graph of Voltage vs Current for Resistor 2 Voltage across [V] Current [mA] 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 Graph of Voltage vs Current for Resistor 3 Voltage across [V] Current [mA] Calculations

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I. The nominal value and tolerance of three resistors 1. Resistor 1 R = (1x10 + 0) x 100 = 1000 Ω The tolerance band is gold which indicates a 5% tolerance, so 950Ω ≤ R ≤ 1050Ω % error = ¿ 985 − 1000 1000 ∨ ¿ x 100% = 1.5 % 2. Resistor 2 R = (2x10 + 2) x 100 = 2200 Ω The tolerance band is gold which indicates a 5% tolerance, so 2090Ω ≤ R ≤ 2310Ω % error = ¿ 2171 − 2200 2200 ∨ ¿ x 100% = 1.3 % 3. Resistor 3 R = (3x10 + 3) x 100 = 3300 Ω The tolerance band is gold which indicates a 5% tolerance, so 3135Ω ≤ R ≤ 3465Ω % error = ¿ 3271 − 3300 3300 ∨ ¿ x 100% = 0.88 % II. Voltage and current values of three resistors 1. The series circuit V = I x R a. Resistor 1 V 1 = 0.159 x 10 -3 x 985 = 0.157 [V] V 2 = 0.315 x 10 -3 x 985 = 0.310 [V] V 3 = 0.470 x 10 -3 x 985 = 0.463 [V] V 4 = 0.625 x 10 -3 x 985 = 0.616 [V] V 5 = 0.781 x 10 -3 x 985 = 0.769 [V] Maximum percent difference of the voltage across resistor 1: % difference = | 0.463 − 0.464 0.463 + 0.464 2 | x 100% = 0.22%

b. Resistor 2 V 1 = 0.159 x 10 -3 x 2171 = 0.345 [V] V 2 = 0.315 x 10 -3 x 2171 = 0.684 [V] V 3 = 0.470 x 10 -3 x 2171 = 1.02 [V] V 4 = 0.625 x 10 -3 x 2171 = 1.36 [V] V 5 = 0.781 x 10 -3 x 2171 = 1.70 [V] Maximum percent difference of the voltage across resistor 2: % difference = | 0.345 − 0.347 0.345 + 0.347 2 | x 100% = 0.58% c. Resistor 3 V 1 = 0.159 x 10 -3 x 3271 = 0.520 [V] V 2 = 0.315 x 10 -3 x 3271 = 1.03 [V] V 3 = 0.470 x 10 -3 x 3271 = 1.54 [V] V 4 = 0.625 x 10 -3 x 3271 = 2.04 [V] V 5 = 0.781 x 10 -3 x 3271 = 2.55 [V] Maximum percent difference of the voltage across resistor 3: % difference = | 2.04 − 2.05 2.04 + 2.05 2 | x 100% = 1% 2. The parallel circuit I = V R a. Resistor 1 I 1 = 1.021 985 = 1.04 x 10 -3 [A] I 2 = 2.02 985 = 2.05 x 10 -3 [A] I 3 = 3.014 985 = 3.06 x 10 -3 [A]

I 4 = 4.01 985 = 4.07 x 10 -3 [A] I 5 = 5.01 985 = 5.09 x 10 -3 [A] Maximum percent difference of the current through resistor 1: % difference = | 2.044 − 2.05 2.044 + 2.05 2 | x 100% = 0.30% b. Resistor 2 I 1 = 1.021 2171 = 0.47 x 10 -3 [A] I 2 = 2.02 2171 = 0.93 x 10 -3 [A] I 3 = 3.014 2171 = 1.39 x 10 -3 [A] I 4 = 4.01 2171 = 1.85 x 10 -3 [A] I 5 = 5.01 2171 = 2.31 x 10 -3 [A] Maximum percent difference of the current through resistor 2: % difference = | 0.471 − 0.47 0.471 + 0.47 2 | x 100% = 0.21% c. Resistor 3 I 1 = 1.021 3271 = 0.31 x 10 -3 [A] I 2 = 2.02 3271 = 0.62 x 10 -3 [A] I 3 = 3.014 3271 = 0.92 x 10 -3 [A] I 4 = 4.01 3271 = 1.23 x 10 -3 [A] I 5 = 5.01 3271 = 1.53 x 10 -3 [A]

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The percent difference of the current through resistor 3: % difference = | 0.31 − 0.31 0.31 + 0.31 2 | x 100% = 0% Answers to Questions Quiz B 1. The equivalent resistance: R = R 1 + 1 1 R 2 + 1 R 3 + R 4 = 1 + 1 1 1 + 1 1 + 1 = 2.5 kΩ = 2500 Ω 2. I total = V/R = 5/2500 = 0.002 [A] 3. I total = I 1 = I 2,3 = I 4 = 0.002 [A] V total = V 1 + V 2,3 + V 4 = 5 [V] (1) V 2,3 = V 2 = V 3 (2) From (1) and (2): V 2 = 5 – V 1 – V 4 = 5 – (0.002 x 1000) – (0.002 x 1000) = 1 [V] I 2 = V 2 /R 2 = 1/1000 = 0.001 [A] The current flowing through R 2 is 0.001 [A] 4. Assume that R 1 and R 2 are connected in parallel, and the voltage across them is equal. Assume that R 3 and R 4 are connected in parallel, and the voltage across them is equal. Then V 1 = V 2 and V 3 = V 4 The ratios of the voltage: V 1 V 3 = V 2 V 4 From Ohm’s law, we get: I 1 x R 1 I 3 x R 3 = I 2 x R 2 I 4 x R 4

Since I 1 = I 3 and I 2 = I 4 , so: R 1 R 3 = R 2 R 4 Assume that R 1 is unknown resistor R x : R x = R 2 x R 3 R 4 [Ω] 5. True

Analysis and Discussion Percent error is low, less than 1.6%. In series circuit, percent difference between measured values and calculated values of voltage is very low, less than 1.1%. In parallel circuit, percent difference between measured values and calculated values of current less than 0.5%. Source of errors might be from an unstable electric current flowing through the circuit, or old equipment also affects the results. The higher the volt, the higher the amperage, so the theory of the formulas for calculating R, V, I (I = V R ) is verified by these experiments. Based on the experimental results, I found that the current through resistors will be equal in series circuit and the voltage across the resistors will be equal in parallel circuit. The purpose of these experiments is achieved. The circuit set-up process has many steps, so it requires high concentration to complete the experiments otherwise we would spend much time to start over. Recording results requires patience and care to avoid errors.

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