Lab 4 (1)

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Apr 3, 2024

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Parallel Circuits Lab #4 EL-100 Work done: 10/16/18 Date of Submission: 10-27-18 Christian Michael, procedure, conclusion Allen Feldmann, purpose, equipment and materials, data, calculations, questions Purpose: In this lab, we created parallel circuits by connecting components to the same node. We used the ammeter to learn how to measure the current flowing through the circuit as a whole, and through individual components of a parallel circuit.

Equipment and Materials: For this lab, we used the XK-150 digital trainer, the BK Test Bench 388A digital multimeter (DMM), around eight pieces of wire, and five resistors with resistances of 470Ω, 680Ω, 1kΩ, 2.2kΩ, and 4.7kΩ. Procedure: Using the trainer, wire up 5 resistors of value: 470Ω, 680Ω, 1kΩ, 2.2kΩ, and 4.7kΩ in parallel to each other. Using the DMM, use the voltmeter to give you a readout as you set the positive to ground dial on the trainer to 10V. Once that is done, make sure to leave a break in the circuit going to ground or coming from the positive, so you can use the Ammeter of the DMM in series with the circuit. Record total current. Turn off the trainer, and close the circuit, then break the circuit before or after the 680Ω resistor, and put the ammeter in series to that resistor within its parallel branch, record the current readout after turning the trainer back on. Rinse and repeat for the remaining 4 resistors. For the next part, I suggest using the positive and negative buses on the breadboard for powering the resistors, it will make it easy. Wire the positive to a row in the breadboard, and wire the positive for the 680Ω resistor to that row, and hook a wire from that row to an ammeter prong, and another wire to the other ammeter prong to the positive bus. In this fashion, as you need to move resistors from the circuit whose current is being read, all you have to do is move the resistor lead from the positive bus to the positive row. Each time turn off the trainer as you change the circuit, hook up components, then turn back on the trainer and record readout. Data: R T 190.4Ω Table 3-3 Measured Value I T 52.1mA I 1 20.87mA I 2 14.79mA I 3 9.96mA I 4 4.56mA I 5 2.11mA

Table 3-4 Measured Current I 6 30.79mA I 7 16.49mA I 8 6.68mA Calculations: Table 3-2 Theoretical Value I 1 I 1 = (E / R 1 ) = 10V / 470Ω = 21.28mA I 2 I 2 = (E / R 2 ) = 10V / 680Ω = 14.71mA I 3 I 3 = (E / R 3 ) = 10V / 1kΩ = 10mA I 4 I 4 = (E / R 4 ) = 10V / 2.2kΩ = 4.55mA I 5 I 5 = (E / R 5 ) = 10V / 4.7kΩ = 2.13mA R T R T = 1/((1/R 1 ) + (1/R 2 ) + (1/R 3 ) + (1/R 4 ) + (1/R 5 )) = 189.91Ω I T I T = (E / R T ) = 10V / 189.91Ω = 52.66mA Conclusion: The percent variation of the measured total resistance from the nominal resistance was roughly +.26%, very close. None of the measured currents had more percent variation than the resistor tolerances. A: Questions 1Q) Compare the measured resistance of Step 2 to the theoretical resistance recorded in Table 3- 2. Determine the percentage variation as shown. 1A) Err = ((R mea - R theo ) / R theo ) * 100% = ((190.4Ω - 189.91Ω) / 189.91Ω) * 100% = .25%

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2Q) Compare the measured currents of Step 4 to the theoretical values recorded in Table 3-2. Indicate which values (if any) have a variation more than resistor tolerance (±5%). Offer an explanation. 2A) I 1 ’s error is -1.93%. I 2 ’s error is .54%. I 3 ’s error is -.4%. I 4 ’s error is .22%. I 5 ’s error is -.94%. 3Q) Refer to the data of Table 3-3 and Table 3-4. 3A) a) I T = 52.1mA. I 1 + I 2 + I 3 + I 4 + I 5 = 52.29mA. b) I 6 = 30.7mA. I 2 + I 3 + I 4 + I 5 = 31.42mA. c) I 7 = 16.49mA. I 3 + I 4 + I 5 = 16.29mA. d) I 8 = 6.68mA. I 4 + I 5 = 6.67mA. 3eQ) Do the above calculations and measurements verify Kirchoff’s current law? Explain your answer. 3eA) Kirchoff’s current law states that ΣI in = ΣI out , so I x should approximately be equal to the summation of the current flowing across all the resistors in that section. For example, since I 6 is measured after the branch containing R 1 , I 6 is a measurement of all current flowing across R 2 , R 3 , R 4 , and R 5 . This is shown with a slight percentage error in the above calculations. B: Personal Conclusions C: Contributions