DC Circuits Lab(4)_ Yip

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Arizona State University *

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132

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Electrical Engineering

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Feb 20, 2024

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1 (1 point) Title of the Experiment: DC CIRCUITS Student’s name: PUURICH YIP Section SLN: 13710 TA’s Name: Sang-Eon Bak, Francesco Setti Week of the experiment: 5 (LAB 4)

2 OBJECTIVE ( 3 points ): The objective of this lab is to simulate simple DC circuits and use them to determine the resistance of pencil lead. These DC circuits will also be used to learn about Kirchhoff ’ s current and voltage laws. EXPERIMENTAL DATA ( 6 points ) & DATA ANALYSIS & RESULTS ( 10 points ) Obtain experimental data that will be used for further calculations from the graphs or tables Be sure to show your calculations and to include related equations and diagrams! PART I. Ohm’s Law . A. Determining the resistance of a pencil lead. • Screen capture of the circuit used for measuring the resistance of the virtual pencil. Figure 1: a simulated circuit, which determines the resistance of the lead in a pencil Internal battery resistance R = 9( Ω ) [See Module 5 on Canvas for R value]

3 V battery (V) 20 40 60 80 100 I PENCIL (A) 0.59 1.18 1.76 2.35 2.94 V PENCIL (V) 14.71 29.41 44.12 58.82 73.53 • Screen capture of the LoggerPro file showing the data table and the plot of I PENCIL vs. V PENCIL and R PENCIL vs. R PENCIL for the virtual pencil, with linear fit. Figure 2: plotted data of an I vs. V graph, and an R vs R graph, which helps determine the resistance of the pencil lead.

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4 m (slope) = 0.040 (A/V); m = 6.9*10^-5 (A/V) - Based on your data conclude whether the virtual pencil was an ohmic element or not. As seen in the LoggerPro graph, the linear fit line is shows a linear I vs V ratio. This tells us that the virtual pencil is an ohmic element. If the graph would ’ ve shown a non-linear relationship, then the element would not be ohmic. B. Virtual pencil lead (VP) ρ = 4.2*10^-4( Ω∙m ); R VP = 24.99 Ω D = 0.6 ( mm );

5 C. Real pencil rod (RP) ρ = 4.2*10^-4( Ω∙m ); 𝑫 ± 𝜟𝑫 = 2.4 ± 0.1 ( mm ); 𝑳 ± 𝜟𝑳 = 18.0 ± 0.1 ( cm ); PART II-1 . Kirchhoff’s Rules V 1 = 10 (Volts); V 2 = 18 (Volts); R 1 = 15 (Ω); R 2 = 8 (Ω); R 3 = 25 (Ω); [See Module 5 on Canvas for V 1 , V 2 , R 1 , R 2 , and R 3 values] • Screen capture of the circuit used for testing the Kirchhoff ’s rules, with the ammeters and voltmeters.

6 Figure 3: Testing Kirchhoff ’ s Laws in a diagonal circuit

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7 PART II-2. Electric Power • Screen capture of the simulation circuit (with closed switch and shown values of the battery and resistors) used for testing the power transfer.

8 Figure 4: A simulation circuit, which will be used to prove the theory of maximum power transfer. • Screen capture of the LoggerPro file showing the data table and the plot of Power vs. Load Resistance with a proper curve fit. Figure 5: LoggerPro graph showing data table and plot of Power vs Load Resistance. V emf ( battery ) = 8 ( Volts ); Internal resistance R S = 4 ( Ω );

9 R Load (Ω) 1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 I (A) 1.6 1.33 1.14 1 0.89 0.8 0.73 0.67 0.62 0.57 0.33 0.24 0.18 0.15 0.12 V Load (V) 1.6 2.67 3.43 4 4.44 4.8 5.09 5.33 5.54 5.71 6.67 7.06 7.27 7.41 7.50 A = 64.14 Watts B = 4.01 Ohms ; 𝜺 = √𝑨 = ……………………… V ; % error of 𝜀 (with battery = 8 V) = • From your fit what value of R L maximizes the power in the load? How does it compare to our simulated internal resistance of the battery set to R S = 4 Ω ? The line of curve fit maximizes the power in the load to 4.01 Ω , which is almost exactly what our simulated internal resistance of the battery was. The load resistance that maximizes the power in R L = B = 4.01 ( Ω ) % error of R L (with R S = 4 Ω ) = • Derivation of the condition for a maximum power transfer in a simple DC Circuit [show work].

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11 DISCUSSION & CONCLUSION ( 10 points ): The purpose of this lab was to simulate DC circuits to learn more about Ohm ’ s Law and find out the resistance of pencil lead. We also explored Kirchhoff ’ s current and voltage laws in a DC circuit, to discover more about the maximum power transfer. We started with the PhET Lab in part 1, in which we designed a circuit with a pencil. This was designed to determine the resistance of the pencil lead. This circuit included: a battery with internal resistance of 9 ohms, a switch, a pencil with lead to simulate resistance, an amp meter, and a voltmeter. We tested 5 values between 20.0-100.0V. It was found that current is proportional to voltage, as seen by the linear nature of Figure 2. This linear nature also tells us that lead in the pencil is an Ohmic element. The plots in figure 2 show that the theoretical resistance of the simulated pencil lead was 24.99 ohms. We were then given values for a real pencil, and the calculations for resistance of the real pencil came out to be 12.19 ohms. In part 2, we created a simple DC circuit which contained 2 loops, each had 1 battery and 1 resistor. These loops were connected with a diagonal wire, and a third resistor. We measured the voltages and currents for each loop. Using Kirchhoff ’ s laws, we found that the sum of the voltages in each loop equaled a value very close to 0V (theoretically should be exactly 0), and the sum of the currents at junctions A and B, also had a value of 0A. We then created another simple DC circuit, with an 8V battery with an internal resistance of 4 ohms, and another resistor. With the second resistor, we simulated load resistance by changing the ohmage in increments of 1 ohm from 1-10 ohms, then increments of 10 from 10-60 ohms. With each change in ohmage, voltage and current were measured, in order to calculate the power of the resistor (P=  battery *I). The plot followed the trend of P=(64.14*R)/(R+4.01)^2, which is the same as P=I^2*R, where I=V/R. In this plot (figure 5), it is shown that the maximum load resistance is 4.01 ohms, and the resistance of our simulation was 4 ohms. This proved the theory of maximum power transfer. These two parts of the lab accurately convey the Ohm ’ s Laws and Kirchhoff ’ s Voltage and Current laws and have proven them to be true.