Introduction to the most common circuit elements: resistor, capacitor, and inductor. Introducing the current-voltage equations for these elements, including Ohm's Law for resistors. Created by Willy McAllister.

The ratio of a sinusoidal voltage to a sinusoidal current is called "impedance". This is a generalization of Ohm's Law for resistors. We derive the impedance of a resistor, inductor, and capacitor. The inductor and capacitor impedance includes a term for frequency, so the impedance of these components depends on frequency. Created by Willy McAllister.

Impedance of 2 elements in series is a complex number. Impedance terminology: reactance, susceptance, admittance. Created by Willy McAllister.

The impedance of capacitors and inductors in a circuit depend on the frequency of the electric signal. The impedance of an inductor is directly proportional to frequency, while the impedance of a capacitor is inversely proportional to frequency. Created by Willy McAllister.

We look at the inductor i-v equations in derivative and integral form. Created by Willy McAllister.

We notice how important it is to give inductor current a place to flow. Created by Willy McAllister.

We give the inductor's kickback current a path to flow by adding a diode. Created by Willy McAllister.

We analyze the inverting op-amp configuration, doing all the algebra from first principles. Created by Willy McAllister.

Demonstration that Kirchhoff's voltage law applies in the frequency domain. The voltage phase offsets around a loop sum to zero. Created by Willy McAllister.

We begin the derivation of the natural response of the LC circuit, by modeling it with a 2nd-order differential equation. Created by Willy McAllister.

Starting from the differential equation, we come up with a proposed exponential solution and plug it into the equation. This gives us a characteristic equation. A "natural frequency" emerges. Created by Willy McAllister.

We use Euler's Formula to change our complex exponential solution into a solution expressed in terms of sines and cosines. Created by Willy McAllister.

In this final step of the derivation, we find two initial conditions and use them to come up with a sinusoidal solution for the LC natural response. Created by Willy McAllister.

We solve the voltage and current of an example LC circuit with given values for L and C, and an initial charge on the capacitor. Created by Willy McAllister.

The inductor-capacitor (LC) circuit is the place where sinewaves are born. We talk about how this circuit works by tracking the movement of an initial charge we placed on the capacitor. Created by Willy McAllister.

We can predict the shape of voltage and current in an LC circuit by tracking the motion of charge as it flows back and forth. Created by Willy McAllister.

Labeling voltages on a schematic is not a matter of "right" and "wrong". It simply establishes how the voltage appears in the analysis equations. Created by Willy McAllister.

Sine and cosine look similar, except they are out of phase. When we talk about sine and cosine as a function of time, the difference is called "lead" or "lag". Created by Willy McAllister.

We complete the solution of a circuit using the mesh current method. Fourth step (solve) out of four. Created by Willy McAllister.