Electronics/LC transient

For a series LC consists of one capacitor connected with one coil in series in a closed loop

Circuit Impedance
In Polar Form
 * $$Z = \omega L \angle 90 + \frac{1}{\omega C} \angle -90$$

In Complex Form
 * $$Z = j\omega L + \frac{1}{j\omega C} $$

Circuit at equilibrium

 * $$L\frac{dI}{dt} + \frac{1}{C} \int I dt = 0$$
 * $$L\frac{dI}{dt} + \frac{1}{C}\times It = 0$$
 * $$L\frac{dI}{dt} = -\frac{It}{C}$$
 * $$\frac{dI}{dt} = -\frac{It}{LC}$$
 * $$\frac{dI}{dt} + \frac{It}{LC}=0$$
 * $$\frac{d^2I}{dt^2} + \frac{I}{LC} = 0$$

Time Constant

 * T = -1/LC

Phase Difference
Phase: A particular appearance or state in a regularly recurring cycle  of changes.

A phase should be used as a problem yet to be discovered. With a tool measuring the distance BC we can for example discover that a certain peculiarity a difference in single circuits theory causes the diagram to carry out its function. Such is the case with AB the same process may take place except a difference in diagram causes a difference in phasing. MAGNETIC coils as mentioned in singularity gives an engineer the means to figure how or where the short might be located. Of course on the basis of general phase the assumed starting point of electricity is found within an oscillation, a point of contact this contact appears different depending on the schematic drawing. In a mathematical notation you can determine using calculus how much power there is in a closed loop. The only problem is to figure a way when the loop is open in what other method can you use to make that solution possible?