AC Circuits

Analysis of AC circuits involves paying attention to not only voltage and current magnitudes, but also to phase shifts. Each circuit element, whether it is a resistor, a capacitor, or an inductor, has an effect on the magnitude of voltage and current and also on the phase shift. AC circuit analysis requires an understanding of the same basic laws as DC circuits (i.e., Ohm’s Law, Kirchoff’s Current Law, and Kirchoff’s Voltage Law) plus an understanding of how to deal with the phase effects of circuit components.

The following set of videos starts with the very basic concepts of what AC voltage and current  are and moves through various concepts in AC circuit analysis. Currently, videos in this series include:

  • Basic Features of AC Voltage
  • Phase Shift in AC Signals
  • Resistors (R), Inductors (L), and Capacitors (C) in AC Circuits
  • Average Voltage
  • Root Mean Square Voltage (and Current)
  • Series Impedance
  • Parallel Impedance
  • Norton and Thevenin Equivalent Circuits
  • Source Transformations

Basic Features of AC Voltage

Technically, AC voltage (or current) can have any waveshape as long as it is periodic and current goes in alternating directions. When first learning about AC voltages, it is much easier to assume that the voltage is sinusoidal. This video describes the characteristics of a sinusoidal voltage such as amplitude, period, and frequency. These are all terms and concepts that you need to gain a solid understanding of before you can begin to analyze AC circuits.

Phase Shift of AC Voltage and Current

The phase shift of a signal is a relative measurement of how much one signal is shifted from another. Typically this phase shift is given in degrees or radians which is more useful for circuit analysis, but the degrees or radians value can also be converted to time.


Resistors, Inductors and Capacitors in AC Circuits

Resistors (R), inductors (L), and capacitors (C) all introduce an impedance in a circuit. Impedance is the AC analog of DC resistance and changes the relationship between voltage and current in two ways (as opposed to one way in DC circuits) – it changes the magnitude and the phase relationship between voltage and current. The magnitude of the impedance is a measure of the ratio of the amplitude of voltage over the amplitude of current. While the phase portion of impedance is a measure of how much phase difference there is between voltage and current.

The following videos go into details about the impedance of individual resistors, inductors, and capacitors.

Average Voltage

The average of an AC signal (whether that is voltage or current) is calculated by integrating the signal over the period and then dividing by the period. A sinusoid that is centered at 0 will have an average voltage of 0.

Root Mean Square Voltage (and Current)

The easiest way to think about oot mean square (RMS) is that it is the DC equivalent value that would give the same amount of power dissipation if applied to a resistor. This video goes into more detail about how it is calculated. For sinusoids, you just have to remember “root 2”

Series Impedance

When components are connected in series, their impedances add together, just like in DC circuits. The difference in AC circuits is that you need to add vectors because impedances have magnitudes and directions.

Parallel Impedance

When components are connected in parallel, the total impedance is equal to the inverse of the sum of the inverse of the individual impedances. Because this is sometimes tricky to do by hand, admittances for components are sometimes used. Watch the video below to learn about admittances and how to use them.

Thevenin and Norton

Thevenin and Norton were great pals who enjoyed analyzing circuits together, however they had totally different approaches. Thevenin liked voltages while Norton liked currents. Watch these videos below and decide who’s method you like better.

Source Transformations

Now that you know whose circuits you like better (Thevenin’s or Norton’s), I’ll show you how to switch back and forth between the two.