PhysicsLab_MiaMartinez

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Feb 20, 2024

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Lab#6: RC Circuit Report Objective :  To virtually observe and measure the factors that affect the time it takes for a capacitor to charge in a direct current (DC) circuit. Part 1– Measured Time vs. Resistance: Data Table#1: C = 50 μF V = 10V Run Resistanc e Measured Time Measured Time Constant Calculate d time constant %Error Unit s Ohms s S s 1 200 0.101 0.0101 0.10 0% 2 400 0.200 0.0200 0.020 0% 3 600 0.299 0.0299 0.030 0.33% 4 800 0.399 0.0399 0.040 0.25% 5 900 0.454 0.0454 0.045 0.89 Graph#1: Measured Time vs. Resistance

Part 2: Measured Time Vs. Voltage Data Table#2 C = _50e-6 F_________ R = ___500 ohms________ Run Voltage Measured Time Measured Time Constant Units V S S 3 0.223 0.0223 5 0.233 0.0233 7 0.243 0.0243 8 0.244 0.0244 10 0.251 0.0251

Graph#2: Measured Time vs. Voltage

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Part3: Charging a Capacitor Plots Data Table#3 C = 50 μF R = 200 ohms= 2.0 kilo ohms V = 10 V Run Elapsed Time Voltage Across resistor Voltage Across capacitor Charge on Capacitor Current Units S V V C A 1 0.012 8.843 1.157 5.79e-5 4.42e-3 2 0.026 7.741 2.251 1.129e-4 3.87e-3 3 0.038 6.873 3.127 1.564e-4 3.44e-3 4 0.050 6.090 3.910 1.955e-4 3.04e-3 5 0.071 4.931 5.069 2.534e-4 2.47e-3 6 0.091 4.025 5.975 2.987e-4 2.01e-3 7 0.118 3.064 6.936 3.468e-4 1.53e-3 8 0.139 2.498 7.502 3.751e-4 1.25e-3 9 0.163 1.951 8.049 4.024e-4 0.98e-3 10 0.233 0.970 9.030 4.515e-4 0.49e-3

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Graph#7: Voltage across the Resistor vs. Current The value of the slope should be the resistance value at the top of Data Table 3 . Calculate the % error of the slope against the resistor value . Please show your calculations below. Percent error: 2000 − 2002.2 2000 × 100 = 0.11 %

The value of the slope should be the capacitance value set in Data Table 3 . Calculate the % error of the slope against the capacitance value . Please show your calculations below. Percent error: 50e-6 − 5e-5 50e-6 × 100 = 0%

Analysis Questions:  Please answer the following questions in at least two complete sentences, unless otherwise indicated. 1. For Part 1 , how is the time constant of the RC circuit τ related to the resistance value? Please explain your observations or shape of the graph. The time constant of the RC circuit is directly proportional to the resistance value. Therefore, the graph is linear because as the time constant increases, the resistance increases as well. 2. For Part 2 , how is the time constant of the RC circuit τ related to the voltage of the battery value? Is the slope large or small? Please explain your observations or shape of the graph. The resistance is not dependent on the resistance, as the slope of the graph was small. Therefore, the graph appeared as a straight line 3. In one sentence only , try to state the factors that truly affect the time it takes to charge a capacitor in a DC circuit [plus resistor ]. Try to explain what affects the charging time and what does not affect it. Any additional sentences will result in point penalties. One sentence only! The charging of a capacitor in a DC circuit depends on the resistance for the capacitor and the capacitance of the capacitor.

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4. Which of the following values in the RC circuit are zero immediately after the switch is closed , or at t = 0 sec when circuit is ON , and which values start at their maximum ? Please explain your choices based on your observations and/or the theory for this lab. a. Voltage drop across the resistor Current and resistance are zero, the charge on the capacitor is at its maximum. b. Voltage measured across the capacitor Time is at its maximum, c. Charge in the capacitor The voltage starts at its maximum, d. Current in the circuit A and D begin at their max values, but gradually decrease. B and C begin at zero, increasing gradually. In the graphs, Charge v. Time and Voltage v. Time resistor begin at a high point, while gradually decreasing. On the other hand, the graphs, Charge v. Time capacitor and Voltage v. Time capacitor begin at a low point, increasing gradually. 5. If a considerable long time has passed after the switch is closed or turned ON , now which of the following values in the RC circuit are zero and which values will be at their maximum ? Please explain your choices based on your observations and/or the theory for this lab. a. Voltage drop across the resistor b. Voltage measured across the capacitor c. Charge in the capacitor d. Current in the circuit The A and D values are closer to zero after observing the circuits, while C and D are high values. In the graphs, Charge v. Time and Voltage v. Time resistance begin at a high point, but end at a low point. After some time, the values get close to zero. In addition, in the graphs Charge v. Time

capacitor and Voltage v. Time, the slope begins at a low point, but reaches a high point. 6. Referring to the four non-linear graphs from Part 3 , try describing each graph based on their shape alone and WITHOUT using any math.  Voltage across Resistor vs. Time The graph curved downward.  Voltage across Capacitor vs. Time The graph resembled a rainbow-like curve.  Capacitor Charge vs. Time The graph resembled a rainbow-like curve.  Current vs. Time The graph was a descending curve. 7. For Part 3 you plotted the voltage drop across the resistor versus the current, what did the slope represent in the circuit and how do you know? Which law/principle does this confirm? Please explain your answer. The slope of the graph represented the resistance in the circuit. This is because of Ohms law and the relationship between voltage and current. 8. For Part 3 you plotted the increasing charge on the capacitor against the voltage across it [capacitor], what did the slope represent for this graph and how do you know? Which part of the theory this confirm? Please explain your answer. The slope of the graph represented the capacitance of the circuit. This is because of the capacitance equation: C=q/V.

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PhysicsLab_MiaMartinez

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