Skip to main content
Engineering LibreTexts

13.1: Introduction

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    This chapter introduces the concept of power and power waveforms in AC systems. This is an important part of AC circuit analysis and turns out to have striking differences compared to the DC counterpart. While it remains true that power is the product of current and voltage, a naive application of that definition can lead to erroneous conclusions for the AC case. In Chapter 1, RMS (i.e., root-mean-square) values were defined and explained. As a general rule, RMS values are used for power calculations, not peak or peak-to-peak values. Further, while complex non-sinusoidal waveshapes are a decided possibility in electronic systems, we shall limit ourselves here to sinusoids.

    One of the tools we shall use is the power triangle. This is a simple trigonometric device designed to illustrate the power relations between resistive and reactive components in a complex impedance. One of its parameters is the power factor, \(PF\). As we shall see, ordinarily we like the power factor to be unity as this implies best use of the available current. It turns out that this is not the case in many systems. As a consequence, we shall also investigate a simple means of compensating or shifting the power factor back to unity. This is known as power factor correction.

    As part of our discussion involving power factor, we shall examine typical applications such as motors. Here we shall consider the power factor of a motor along with its efficiency. The efficiency is defined as the useful output power relative to the supplied power and is always less than 100%. Finally, we shall consider basic power factor correction for this application.

    One practical item to remember here is that, while the instantaneous power changes over time due to the sinusoidal cycling of the voltage and current, what matters to most electrical and electronic devices is the production of internal heat. Devices such as resistors, transistors and so forth, have mass, and thus exhibit a thermal time constant. That time constant tends to be much longer than the period of the wave. The effect is an averaging of the power waveform. In other words, components do not heat up and cool down instantaneously, any more than a hot fry pan would drop to room temperature the moment it was removed from its burner.

    13.1: Introduction is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by James M. Fiore.

    • Was this article helpful?