Speed of Light Derivation

The speed of light may seem like an arbitrary constant of nature but, in some sense, it is actually set by other properties of the world. These other properties are the strengths of the electric and magnetic fields which are defined by the constants that are used in determination of them, otherwise known as the permittivity constant ($\inline&space;\epsilon_0=8.85&space;\times&space;10^{-12}&space;\texttt{&space;}\textup{F/m}$) and permeability constant ($\inline&space;\mu_0=4\pi&space;\times&space;10^{-7}\texttt{&space;}\textup{H/m}$). Because light is simply an electromagnetic wave, one can derive its speed using these constants. Continue reading Speed of Light Derivation

Complex Impedance

There is a certain luxury of circuit calculations for systems contain direct current that alternating current systems really do not have. It is the idea that voltage and current are “synced.” An increase in voltage will create a corresponding increase in current seemingly instantaneously. However, an alternating current that experiences voltage oscillations experiences a delay. This can mean voltage is at the highest point in its fluctuations while current only reaches such a point a little bit later at which point voltage might already be at its lowest. The ratio of voltage to current is also unclear in these circuits. This makes it hard to describe the system easily. Continue reading Complex Impedance

Complex Exponentials

Complex exponentials are used immensely in math and as a result, in many fields of science. It is also used in abundance throughout this site so it is important to understand what they are for future reference. They show the relationship between exponentials and trigonometry on a fundamental level. The following is the relationship.

$e^{ix}=\textup{cos}(x)+i\textup{sin}(x)$ Continue reading Complex Exponentials