AC Transients in an RC Circuit

by Alexander Terk

Submitted : Spring 2013

This project was designed to introduce the concepts of an RC Circuit. More specifically, to understand the transient behavior of the specific circuit that is proposed. First, I had to relate the given equation to the behavior of the circuit. I did this by rearranging the variables to let the AC voltage source govern the circuit. Next I was given the task to solve the equation in terms of the capacitor charge, related to time. This was done by using the solution given for such a first order linear differential equation, and relating it to the equation I obtained through the previous steps. Once this equation was formed, the project description explained that it was necessary to find the derivative of it, which would give me the equation for current. This was done using the general rules for differentiation. After all of the calculus was done, it was necessary to plot the graphs of the solved equations on a graph and answer the given prompts. From the results, I concluded that the time it takes for the potentially dangerous transient behavior to die off is extremely minimal.

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