How to do the Math of LC Circuits

Interesting things happen when you combine loops of wire and metal plates in series. Inductors and capacitors together create AC currents at tunable frequencies, which in principle is the essence of our wireless society. In classical physics, the easiest way to create electromagnetic radiation is to accelerate (such as by shaking) electric charges, and that is exactly what you have in an AC current. Check this out to remind you of the math, and how LC circuits are the equivalent of simple harmonic motion of masses on springs from mechanics.

How to Find Charge on Capacitors in Circuits

There are a lot of parallels (ha, ha) between resistor and capacitor circuits. For resistor circuits, we tend to re-draw the circuit as a series circuit in order to find the voltage differences across parallel sets of resistors. This allows us to then find how the current splits in any parallel sets. We do basically the same thing for capacitor circuits, where we re-draw the circuit as a series, find the voltages, and then go and find how the stored charge splits on parallel branches. Here is an example of this process.