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Graphs of Absolute Value Equations

Graph two-variable absolute value equations

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Credit: Daniel Christensen
Source: http://commons.wikimedia.org/wiki/File:Inside_of_a_Boss_Audio_DD3600_Class_D_mono_block_amp.jpg
License: CC BY-NC 3.0

Are you familiar with direct current (DC) and alternating current (AC)? You deal with them all the time. Batteries usually provide DC current, while all your electric wall outlets supply AC current. But many of your electronic devices use DC power. How do these DC devices work when the supply power is AC? There must be some conversion occurring, right? That's where rectifiers come in.

Why They’re Important

AC-to-DC converters are either built inside devices or made part of the power cords. Check the adapters of your laptop, phone charger, or other appliances; most of them will show the input as AC and output as DC.

Credit: Laura Guerin
Source: CK-12 Foundation
License: CC BY-NC 3.0

Now what does a rectifier do? In the figure above, Graph 1 depicts an AC waveform. Voltage is on the \begin{align*}y\end{align*}-axis, and time is along the \begin{align*}x\end{align*}-axis (which is unmarked in the figure but runs through the middle of each coordinate plane). What this curve shows is that the voltage alternates between positive and negative values over time—hence the name “alternating current.” If you build a circuit that only allows the positive values through but nullifies the negative values, you would obtain Graph 2. This is accomplished by a half-wave rectifier. If you have a circuit that outputs the absolute values of the inputs, then you'd arrive at Graph 3. This is accomplished by a full-wave rectifier.

In addition to AC-to-DC transformations, rectifiers have many other uses as well. Take a look:

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To learn more about rectifiers and what they do to electric currents or voltages, check out the following videos.



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Image Attributions

  1. [1]^ Credit: Daniel Christensen; Source: http://commons.wikimedia.org/wiki/File:Inside_of_a_Boss_Audio_DD3600_Class_D_mono_block_amp.jpg; License: CC BY-NC 3.0
  2. [2]^ Credit: Laura Guerin; Source: CK-12 Foundation; License: CC BY-NC 3.0

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