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May 14, 2024

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Lab #6: Voltage, Current, and Resistance II PHYS-UA12 Professor S. Yu

1 Objective and Description In this experiment, students are able to expand upon knowledge of voltage, current, and resistance from lecture and the previous lab. In part I of this experiment, resistors are measured in series and parallel. This is also observed in this experiment but rather than taking three different measurements, AC capabilities of the signal generator are used to obtain continuous measurements of current and voltage. This is accomplished through the use of the virtual simulation database from phet.colorado.edu. Theory There are a few significant equations from the previous lab that are still relevant. One such is Ohm's law, where V=IR. Additionally, there is a difference in resistance depending on if it is in parallel or series. If 2 resistors are connected in series, the equivalent as a single resistor is R=R 1 + R 2 . If 2 resistors are connected in parallel, the equivalent to a single resistor is . 1 𝑅 = 1 𝑅 1 + 1 𝑅 2 Procedure Using the virtual simulation database, a 33Ω and 100 Ω resistors are connected in series. Using the voltmeter, the resistance is found for applied voltages of 1 through 7. This is compared to the theoretical values that are calculated using Ohm’s Law. It is important to note the placement of the voltmeter and current meter. In order to measure the voltage, the voltmeter must be placed in parallel across the device. To measure the current, the current meter must be in series. In series, the overall resistance value of the circuit is found using the current obtained from the analog current meter for the DC voltages of 1 through 7. Next, the resistance values are calculated for the same resistors in parallel and compared to the theoretical value. The applied DC voltages of 1 V to 7 V are used again. Data and Calculations

2 Resistors in Series Voltage (V) Current (A) Resistance (R=V/I) (Ω) Theoretical Resistance 1 0.008 125 R=R 1 +R 2 =33Ω+100Ω =133Ω 2 0.015 133.33 3 0.02 150 4 0.03 133.33 5 0.04 125 6 0.05 120 7 0.05 140 Table 1 . Resistors in Series Figure 1. Voltage vs. Current for Resistors in Series Resistors in Parallel Voltage (V) Current (A) Resistance (R=V/I) (Ω) Theoretical Resistance 1 0.04 25 1 𝑅 = 1 𝑅 1 + 1 𝑅 2 2 0.08 25

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3 1 𝑅 = 1 33 + 1 100 1 𝑅 = 0. 0403 R=24.81 3 0.12 25 4 0.16 25 5 0.20 25 6 0.24 25 7 0.28 25 Table 2. Resistors in Parallel Figure 2. Voltage vs. Current for Resistors in Parallel Figure 3. Simulated Circuit of Varying Resistances in Series and Parallel with battery voltage of 10V.

4 Resistors in Circuit (Figure 3) Resistor Resistance (Ω) Voltage Across Resistor (V) Current (A) (I=V/R) R 1 10 6.02 0.602 R 2 10 3.98 0.398 R 3 11 2.24 0.204 R 4 15 1.75 0.117 R 5 10 0.87 0.087 R 6 20 0.87 0.044 R 7 13 0.56 0.043 R 8 5 0.06 0.012 R 9 10 0.31 0.031 R 10 20 0.25 0.013 Table 3 . Questions 1. A wire with a resistance of 2.5 ohms is stretched to twice its length. The cross sectional area is cut in half. What is the resistance of the new wire? R= ⍴ =2.5 R’= ⍴ → R’=4 ⍴ =4•2.5 = 10 Ω 𝐿 𝐴 2𝐿 .5𝐴 𝐿 𝐴 2. 100 volts is being applied to a device that has a power of 20 watts. The voltage being applied now changes to 50 volts. How much current is it drawing now? P=VI → 20=50I → I=0.4A 3. The temperature of a copper wire immersed in a non conductive fluid is lowered. What is occurring to the resistance of the copper wire?

5 Resistance of a conductor is directly proportional to temperature. Since the temperature decreases, the resistance also decreases. 4. You have a 10 ohm resistor connected in series with an ammeter. The voltage applied to the whole circuit is 1.2 volts. At the same time you have a voltmeter connected across the 10 ohm resistor and voltmeter reads 0.9 volts. The circuit draws a total of 0.5 amps. Can you determine resistance of the ammeter? Next, you change the scale of the ammeter and overall current in the circuit drops. Also, the voltage across the 10 ohm resistor drops. What occurs to the resistance of the ammeter? Voltage across ammeter = 1.2V-0.9V = 0.3V ; Current =0.5V R amm = Ω 𝑉 𝐼 = 0.3 0.5 = 0. 6 Since R amm is inversely proportional to current, I, as the overall current decreases, the ammeter resistance increases. 5. Build a circuit that contains a 10V battery and some number of 2 ohm resistors, such that the current flowing through the battery is 3.75 amperes. Either include a screenshot of this circuit in your lab, or else draw a schematic circuit diagram showing what this circuit looks like.

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6 Error Analysis Since a virtual simulation is being used, there is little presence of human error. One possible error one could make is connecting the ammeter in parallel, rather than series. When comparing the values obtained in the simulation to the calculated theoretical values (Table 1 and Table 2), the theoretical values are lower. For the resistors in series (Table 1), there was more variance in the values, with larger percent errors, than compared to that in parallel (Table 2). Conclusion Through this experiment, the relationship between voltage, current, and resistance became more transparent. I was also able to become familiar with the PhET simulation database. By building the circuits virtually, it also became easier to see the difference between a circuit built in parallel and in series. Resources

7 Halliday, David, Robert Resnick, Jearl Walker. Fundamentals of Physics , 11th Edition. Wiley, 05/2018. VitalBook file. https://phet.colorado.edu/sims/html/circuit-construction-kit-dc-virtual-lab/latest/circuit-construction-kit-d c-virtual-lab_en.html Salvati, Michael. Mincer, Allen. Experiment #6: Voltage, Current, and Resistance II . General Physics II. New York University. https://physics.nyu.edu/~physlab/GenPhysII_PhysIII/Final_drafts_GPII_Labs/Voltage-Current-R esistance-II-12-12-2016-New-York.pdf