This eBook was written as the sequel to the eBook titled DC …
This eBook was written as the sequel to the eBook titled DC Circuits, which was written in 2016 by Chad Davis. This eBook covers Alternating Current (AC) circuit theory as well us a brief introduction of electronics. It is broken up into seven modules. Module 1 covers the basic theory of AC signals. Since only DC sources are used in the first eBook, details of AC signals such as sinusoidal waveforms (or sine waves), square waves, and triangle waves are provided. Module 2, titled AC Circuits Math Background, covers the mathematics background needed for solving AC circuit problems. The background material in Modules 1 and 2 are combined in Module 3 to solve circuits with AC sources that include resistors, inductors, and capacitors (RLC circuits).
Solving circuits with differential equations is hard. If we limit ourselves to …
Solving circuits with differential equations is hard. If we limit ourselves to sinusoidal input signals, a whole new method of AC analysis emerges. Created by Willy McAllister.
Here's a preview of how AC analysis is going to work. To …
Here's a preview of how AC analysis is going to work. To get ready we need to review some of the ideas from trig and complex numbers. Created by Willy McAllister.
We break a sinusoidal input voltage into two complex exponentials. Using superposition, …
We break a sinusoidal input voltage into two complex exponentials. Using superposition, we can recover the complex output signals and reassemble them into a real sinusoidal output voltage. Created by Willy McAllister.
This new version of the CCK adds capacitors, inductors and AC voltage …
This new version of the CCK adds capacitors, inductors and AC voltage sources to your toolbox! Now you can graph the current and voltage as a function of time.
Build circuits with capacitors, inductors, resistors and AC or DC voltage sources, …
Build circuits with capacitors, inductors, resistors and AC or DC voltage sources, and inspect them using lab instruments such as voltmeters and ammeters.
Students are introduced to several key concepts of electronic circuits. They learn …
Students are introduced to several key concepts of electronic circuits. They learn about some of the physics behind circuits, the key components in a circuit and their pervasiveness in our homes and everyday lives. Students learn about Ohm's Law and how it is used to analyze circuits.
A closer look at the complex exponential term in Euler's Formula. We …
A closer look at the complex exponential term in Euler's Formula. We see that it represents a complex number, a distance of 1 from the origin of the complex plane. Created by Willy McAllister.
When we put time in the exponent of a complex exponential, the …
When we put time in the exponent of a complex exponential, the complex number it represent rotates in a circle on the complex plane. You can think of it as a spinning number! Created by Willy McAllister.
Complex numbers can be represented three ways on the complex plane: cartesian …
Complex numbers can be represented three ways on the complex plane: cartesian coordinates, radius and angle, and exponential form. Created by Willy McAllister.
Multiplying a real or complex number by the imaginary unit j corresponds …
Multiplying a real or complex number by the imaginary unit j corresponds to a rotation by +90 degrees. This is the key feature of j that makes it such a useful number. Created by Willy McAllister.
Euler's formula relates the complex exponential to the cosine and sine functions. …
Euler's formula relates the complex exponential to the cosine and sine functions. This formula is the most important tool in AC analysis. It is why electrical engineers need to understand complex numbers. Created by Willy McAllister.
The ratio of a sinusoidal voltage to a sinusoidal current is called …
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.
The impedance of capacitors and inductors in a circuit depend on the …
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.
Demonstration that Kirchhoff's voltage law applies in the frequency domain. The voltage …
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.
Sine and cosine look similar, except they are out of phase. When …
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.
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