Challenge¶
In this challenge, you will analyze "both halves" of the capacitor charge/discharge circuit that we discussed in Reading 11. As before, this circuit could be analogous to many larger systems with components that are scaled up to either store or "use" (dissipate) energy. For us, let's continue to imagine that the constant voltage source (5V) is "on sometimes, off sometimes," perhaps because it is a renewable source of power like wind or solar, and that the capacitor is some kind of energy storage system designed to prevent interruptions to the power grid, represented here by the second resistor and the LED light.
To simplify the system, I have removed the LED light (which has some strange characteristics that we will need to discuss at a later time). The second resistor $R_2$, also a $5K\Omega$ resistor, now represents the "load" on the power grid, which could represent power usage from houses, factories, electric vehicle charging stations, etc. on a full-size grid. We will now ask the question:
What happens when the renewable source ($V_{in}$) stays on, and the load is activated? How much voltage $V_{1c}$ gets stored in the capacitor, and how fast does the storage occur? Note that because we are asking about the temporal (time-dependent) behavior of a system that includes an energy storage device, we will be looking for a differential equation!
To analyze the system, we will first draw its schematic.
Assignment¶
Assuming the capacitor begins in a fully discharged state ($V_{1c}=0$), scope, develop, and evaluate a model of the system as the capacitor charges and the "load" represented by $R_2$ is powered.
Deliverable: System Scope¶
Present your system scoping steps below
YOUR ANSWER HERE
Deliverable: Model Construction¶
Using what you know, develop a model for the system as defined by your scope. You know the following:
- $V_{in}$ is a constant $5V$ at the start of the charging/power simulation
- The voltage $V_{c1}=0$ relative to ground at the start of the simulation
- $R_1 = R_2 = 5000 \Omega$
- $C = 100x10^{-6} F$
YOUR ANSWER HERE
Deliverable: Model Evaluation¶
Using the datafile: reading12data.txt, with time as the first column and capacitor voltage as the second, evaluate your model for accuracy.
% YOUR CODE HERE
error('No Answer Given!')
Deliverable: Model Comparison¶
Using what you have learned from your modeling steps above, compare the situation described in Reading 11 with the situation described in this notebook. Include a plot of the test from reading 11, provided as capchargedata.txt comparing that test to your simulation, and to the data provided in reading12data.txt.
Discuss differences in available energy, as well as any potential differences in how long the capacitor takes to get to its "steady state" or final voltage value. Use the model equation you developed to help with this, and feel free to include extra code cells below to perform calculations and help you make any comparisons you feel are appropriate. What implications do these differences have for a power grid?
YOUR ANSWER HERE
% YOUR CODE HERE
error('No Answer Given!')