Morrow Dc Circuit Lab

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Sierra College *

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210

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Physics

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Apr 3, 2024

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Physics 210L Fall 2021 Sunderland L Morrow 11-05-21 1 DC Circuit Analysis (40pts) Introduction The principal goal in this experiment is to reinforce the fundamentals of dc circuit analysis and basic wiring skills. In this lab, you will apply your knowledge of series and parallel circuits and Kirchhoff’s laws to a simple bridge circuit. The experimental objectives of this three-part activity are: Part 1,2: To learn how to wire series and parallel circuits. Part 1,2: To learn about Kirchhoff’s current and voltage laws. Set R1=100 W , R2=240 W , R3=470 W , and R4=200 W Part 1 Procedure 1. Measure the value of the resistors with the multimeter. Use multimeter manual to determine the uncertainty in the measurement (see Appendix). Record the measured values in Table 1. 2. Using the “PROTO-BOARD,” wire the circuit shown below. Set the DC power supply voltage to approximately 6.0V. Take a picture of your circuit and paste it before Table 1. Measure and record its value in Table 1. 3. Measure and record, I S , the current through the power supply. Use multimeter manual to determine the uncertainty in the measurement (see Appendix). 4. Measure and record the potential difference across R1, R2, R3, and R4. Use multimeter manual to determine the uncertainty in the measurement (see Appendix). Analysis 1. Calculate, I R1 , the current through R1 and I R2 , the current through R2 along with their uncertainties and record their value in Table 1. Apply Kirchhoff’s current law to calculate I S along with its uncertainty. Finally calculate the percent difference between latter value and measured value I S . Record your results below Table 1. Show all your work below. Experiment 4 A B C D V

2 2. Calculate, I R3 , the current through R3 and I R4 , the current through R4 along with their uncertainties and record their value in Table 1. Apply Kirchhoff’s current law to calculate I S along with its uncertainty. Finally calculate the percent difference between latter value and measured value I S . Record your results below Table 1. Show all your work below. Part 2 Procedure 1. Place the multimeter between points A and C (refer to the figure below). Set the multimeter to the 10A scale, and measure and record the current I AC (along with its direction) through the meter. If this scale setting is too large to give a non-zero value, try a lower scale setting. Take a picture of your circuit and paste it before Table 2. 2. Leave the multimeter between points A and C and measure and record, I S , the current through the power supply. Record your results in Table 2. Do you expect the same current as in Part 1? Why? 3. Measure and record the potential difference across R1, R2, R3, and R4. Use multimeter manual to determine the uncertainty in the measurement (see Appendix). 4. Repeat steps 1 through 3 but this time set the multimeter that is between points A and C to the lowest possible current setting. Do you expect any values to change? Why? Record your results in Table 3. Analysis 1. Calculate, I R1 , the current through R1 and I R2 , the current through R2 along with their uncertainties and record their values in Table 2. Apply Kirchhoff’s current law to calculate I S along with its uncertainty. Finally calculate the percent difference between latter value and measured value I S . Record your results below Table 2. Show all your work below. 2. Calculate, I R3 , the current through R3 along with its uncertainty and record its value in Table 2. Use your calculated value of I R3 and an appropriate current from Step 1 along with Kirchhoff’s current law to calculate I AC and its uncertainty. Finally calculate the percent B A C D V

Physics 210L 3 difference between the latter value and measured value I AC . Record your results below Table 2. Show all your work below. 3. Calculate, I R4 , the current R4 through along with its uncertainty and record its value in Table 2. Use your calculated value of I R4 and an appropriate current from Step 1 along with Kirchhoff’s current law to calculate I AC and its uncertainty. Finally calculate the percent difference between latter value and measured value I AC . Record your results below Table 2. Show all your work below. 4. Using the results in Table 3, calculate the current through each resistor along with their uncertainties. Show your work below. Data and Results Part 1 Table 1 R±δR (kΩ) V±δV (Volts) I ±δ I (mA) R1 0.0983 ± 0.0007 1.099 ± 0.006 11.2 ± 0.1 R2 0.239 ± 0.001 3.424 ± 0.007 14.34 ± 0.07 R3 0.464 ± 0.001 5.165 ± 0.008 11.14 ± 0.03 R4 0.1979 ± 0.0009 2.838 ± 0.006 14.34 ± 0.07 Power Supply Voltage ( 6 .291 ± 0 .008)࠵? I S ±δ I S = ( 25 .3 ± 0 .2 )࠵?࠵? ࠵? = ࠵? ࠵? ࠵? !" = 1.099࠵? 0.0983kΩ = 11 .2࠵?࠵? Sample calculation for propagation: δ I R1 = : ; #$ !" #! ࠵?࠵?> % + ; #$ !" #& ࠵?࠵?> %

4 δ I R1 = : ;− & ! # ࠵?࠵?> % + ; " ! ࠵?࠵?> % δ I R1 = :;− ".()) ((.()+,) # 0.0007> % + ; " (.()+, 0.006> % δ I R1 = : ;− ".()) (.((). . % 0.0007> % + (0.0 6 1) % δ I R1 = : ;− (.((( / . (.((). . % > % + (0.0 6 1) % δ I R1 = A(−0.0 7 8) % + (0.0 6 1) % δ I R1 = √0.00 6 0 + 0.00 3 7 δ I R1 = √0.00 9 7 δ I R1 = 0.0 9 8 δ I R1 = 0 .1࠵?࠵? Kirchhoff’s current law for ࠵? 0 : ࠵? !" + ࠵? !% = ࠵? !, + ࠵? !1 ࠵? 0 = ࠵? !, + ࠵? !1 ࠵? 0 = 11.14࠵?࠵? + 14.34࠵?࠵? = 25 .48࠵?࠵? Example calculation for propagation: δI 0 = F G ࠵?࠵? 0 ࠵?࠵? !, ࠵?࠵? !, I % + G ࠵?࠵? 0 ࠵?࠵? !1 ࠵?࠵? !1 I % δI 0 = A(࠵?࠵? !, ) % +(࠵?࠵? !1 ) % δI 0 = A(0.03) % +(0.07) % δI 0 = √0.000 9 + 0.00 4 9 δI 0 = √0.00 5 8 δI 0 = 0.0 7 6 δI 0 = 0 .08࠵?࠵? Percent difference sample calculation: [|25.48࠵?࠵? − 25.33࠵?࠵?|] - 25.48࠵?࠵? + 25.33࠵?࠵? 2 / ∗ 100% = 0.1 5 - 50.8 1 2 / ∗ 100% = 0.1 5 25.4 0 2 ∗ 100%

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