Circuits

Current is the flow of electric charge, is measured in Amperes, and is denoted by . Current flows from positive to negative, but electrons flow opposite to the flow of the current. Current only flows over a potential difference (high to low).

Resistance ()
Resistance, measured in Ohms (denoted by the capital Greek letter omega: ), is a measure of… resistance of a current.

A capacitor is a way to store electric potential energy in an electric field. The capacitance of a capacitor depends only on the capacitor’s physical characteristics (like the shape or the material to separate the plates). A parallel-plate capacitor is the simplest kind. The resistance of a wire is directly related to its length and inversely related to its cross-sectional area. — is the resistivity constant, and depends on the material.

Circuit Diagrams

Series Circuits
Circuits in series are circuits with only one path for the current to take.

Capacitance ()
Magnitude of on one plate divided by between the 2 plates: Always positive. Also, the total charge on a capacitor is zero. This is getting complicated, but the units for capacitance are Farads, or Coulombs / Volts, or… Don’t ask me, I didn’t come up with this. If we do a little funny, we get that the capacitance of a parallel-plate capacitor is This assumes that there is a vacuum between the two plates. However, if we use an insulating material between the two plates, we use a different and therefore increase the capacitance of the capacitor. The insulating material is called a dielectric. The polarization of the dielectric creates an electric field opposite to the original one, which means that the total electric field in between the plates is reduced. Since and the capacitance increases.

In parallel, the total capacitance is equal to the sum of the individual capacitances in parallel. Reciprocal of the sum of reciprocals in series.

We can determine the effect of the dielectric with the dielectric constant, which equals the ratio of the dielectric’s electric permittivity to the permittivity of free space. The electric permittivity of a material is a measurement of how much a material is polarized when it is placed in an electric field.

Kirchhoff Laws
Hardest part about this is the name.

Kirchhoff’s Loop Rule

Essentially, this is conservation of electric potential energy in a closed loop. It’s like dropping an object and then returning it to where it started: no change!

Kirchhoff’s Junction Rule
The charge entering a junction must be the same as the charge leaving a junction:

Now that we know about capacitors n shit, let’s talk about RC circuits and how, sometimes, changes in , and aren’t instantaneous.

todo: what was this…

Time constant is whatever is under the fraction in (i.e. in this case).