Refining and Optimizing Analytical Models
Completion requirements
This section gives an example of how the model developed earlier could be extended to account for additional knowledge of the system's structure. Again, if you have not yet been exposed to this particular type of mathematical analysis, simply note that all models can be refined as we gain more knowledge about the system. Think back to the model you identified in the last section. How could you extend this model to make it a better reflection of reality?
Mathematical model
Calculation
The mathematical model is
\(\dfrac{dV}{dt}=\dfrac{I}{C}\), \(V(0) = 0\),
\(\dfrac{dI}{dt} = \dfrac{-V}{L} - \dfrac{RI}{L} + \dfrac{V_B}{L}\), \(I(0) = 0\),
where \(V_B=5V\), \(R=0.1Ω\), \(L=4×10^{−9}H\), and \(C=0.5×10^{−9}F\).