Everything you always wanted to know about oscillating circuits and more.

LCR circuits might seem daunting; I would suggest viewing them as LC circuits with a small resistor tacked on. As we learned earlier, the LC combination produces oscillations! The inductor (L) stores energy -in its magnetic (B) field- when there is any current in the circuit; while the capacitor, on the other hand, stores energy -in its charge and the associated E field-  when the current in the circuit is zero....  There is always energy somewhere, and it transfers back-and-forth, from the inductor to the capacitor, in an oscillatory fashion.

A small resistor adds a third element which transfers energy out of the circuit, e.g., into light and/or heat. We can regard the resistor as a small perturbation that gradually diminishes the energy in the circuit; with each oscillation the peak values of the charge and the current are a little less than they were the time before.

Below are some notes -calculations- which show a fundamental model equation for an LCR circuit and its solution in terms of Q(t). The main things you need to know are:

1) what the equation for Q(t) is; what its graph looks like -in detail-; and how its parameters and behavior depend on L, C and R.

2) same thing for the current, I(t). Additionally, the relationship, graphical and in equation form, between I(t) and Q(t) is important.

3) how to calculate energy from I(t) and Q(t).

4) how to calculate w, T and tau from L, C and R, and what they are and what role they play in Q, I, V and all related energies.

and additionally,

4) to have an intuitive feel for and understanding of the characteristic time scales-- tau and T -- and to understand what it means for tau to be much greater than T.

Your comments and questions are welcome!