Calculate t for capacitors in parallel and in seriesCharging and discharging The image presents a graph and a data table from an experiment labeled "Lab 5 Parallel 0.5mic...". The graph displays the potential (V) on the y-axis versus time (s) on the x-axis. The red curve indicates an exponential relationship representing the potential over time.### Graph Details:- **X-axis:** Time (s), ranging from 0 to 7 seconds.- **Y-axis:** Potential (V), with a range from 0 to 4.5 volts.- The graph follows the equation: \( y = a \exp(-cx) + b \).- Parameters: - \( a = -4.815 \) - \( b = 4.591 \) - \( c = 0.9738 \) - RMSE (Root Mean Square Error) = 0.03482### Data Table:The table titled "Data Set 1" lists time versus potential values. | Time (s) | Potential (V) ||----------|-----------------|| 0.0 | 0.008547009 || 0.1 | 0.118437118 || 0.2 | 0.548229548 || 0.3 | 0.935286935 || 0.4 | 1.285714286 |This experiment appears to study the behavior of potential over time, modeled by an exponential decay function. The fit suggests a precise model with a low RMSE, indicating a strong agreement between the experimental data and the model. ### Lab 5: Parallel 0.5 Micron Experiment#### Graph AnalysisThe graph displays a time-dependent potential decay, showcasing an exponential decrease in potential over time. The x-axis represents time in seconds (s), ranging from 0 to approximately 7.1 seconds. The y-axis represents the potential in volts (V), starting from around 4.5 volts.The plotted data illustrates a red curve representing the potential (V) decaying sharply initially and gradually leveling off as time progresses.#### Exponential Decay FunctionThe graph is accompanied by a mathematical model expressed as:\[ y = a \cdot \exp(-c \cdot x) + b \]- **x-range**: 0.0 - 7.1 seconds- **Parameters**: - \( a = 4.823 \) - \( b = 0.004601 \) - \( c = 0.9731 \) - **RMSE (Root Mean Square Error)**: 0.03669These parameters define the exponential decay curve fitted to the data, indicating the influence and rate of decay over time.#### Data Set 1| Time (s) | Potential (V) ||----------|-------------------|| 0.0 | 4.581196581 || 0.1 | 4.490842491 || 0.2 | 4.059829060 || 0.3 | 3.670329670 || 0.4 | 3.321123321 |This table provides a sample of time points with their corresponding potential values, illustrating the rapid decay in the beginning phase of the experiment.#### ConclusionThe experiment demonstrates the exponential decay of potential over time, modeled effectively by the given parameters, reflecting the behavior of a parallel circuit with a 0.5-micron component. This analysis is crucial for understanding the kinetics in various scientific and engineering applications.

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Science

Physics

Calculate t for capacitors in parallel and in series Charging and discharging

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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