We solve a circuit by writing Kirchhoff's Voltage Law in terms of "mesh currents." This video covers the first three steps out of four. Created by Willy McAllister.

Successive powers of the imaginary unit j correspond to a rotation. Created by Willy McAllister.

The concept of negative frequency is perplexing, but it makes sense when you think about rotating complex exponentials.

Last step of the Node voltage method for analyzing circuits: Solve the system of simultaneous equations. Created by Willy McAllister.

The Node Voltage Method solves circuits with the minimum number of KCL equations. Steps 1 to 4 out of 5. Created by Willy McAllister.

An op-amp can be used to amplify a voltage. The gain is determined by the ratio of two resistors. Created by Willy McAllister.

We derive the natural response of an RC circuit and discover it has an exponential form. Created by Willy McAllister.

An example of the exponential natural response of an RC circuit, with real component values. Created by Willy McAllister.

We put some charge on a capacitor in an RC circuit and observe what happens to the voltage and current. This is called the natural response. Created by Willy McAllister.

An example solution of an RC step response, with real component values. Created by Willy McAllister.

An RC circuit responds to a step of voltage with a smooth transition between the starting and ending voltage. The RC step response is a fundamental behavior of all digital circuits. Created by Willy McAllister.

The RC step response is an exponential curve. We set up the circuit and create the differential equation we need to solve. We introduce the technique of Natural response + Forced response. Created by Willy McAllister.

We find the RC step response using the method of Natural + Forced response = Total response. Created by Willy McAllister.

Resistors connected head-to-tail are in series. The equivalent overall resistance is the sum of the individual resistance values. Created by Willy McAllister.

The sign convention for passive components defines what we mean by positive and negative voltage and current. Created by Willy McAllister.

A systematic approach to simplify a complicated resistor network by looking for series and parallel resistor patterns. Created by Willy McAllister.

Sine and cosine can be generated by projecting the tip of a vector onto the y-axis and x-axis as the vector rotates about the origin. Created by Willy McAllister.

If we introduce time as the argument to the sine function, we get a sine wave. Animated. Created by Willy McAllister.

Voltages and currents often have an exponential shape. We look at some properties of exponential curves and learn how to rapidly sketch accurate waveforms. Created by Willy McAllister.