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Alternating current and its relation to voltage

Published on 05 January 2023, updated on 10 January 2023 - electronics technology


For a while now I am interested in electronics. So after some false starts, I started following a long course on it: Crash Course Electronics and PCB Design.

Lecture 9 was about alternating current (AC), the kind of current that flows from a wall socket. I struggled to understand how it's voltage is determined, so I took a lot of notes. This is the result.

Warning: algebra ahead. Also: everything here may be wildly inaccurate. Did I mention that I am just learning this stuff?

What is alternating current

Alternating current measn that the supply source voltage changes as a function of time. In general, this is a sine wave, with positive high peak voltages and negative low peak voltages.

A negative voltage means that the current flows in the opposite direction, from minus (-) to plus (+). In the span of a full sine wave, the current changes direction twice. So with a standard 60Hz alternating current, the current changes direction 120 times per second.

Properties of alternating current

Alternating current has a few commonly-used properties:

In the rest of this note, we will work with an AC voltage with the following properties:

Root Mean Square Voltage

Root Mean Square (RMS, wikipedia) is a formula that is often used whencalculating the voltage over time for an alternating current circuit.

Its definition is as follows:

$$ f(rms) = \lim_{T \to \infty} \sqrt{\frac{1}{T} \int_0^T [f(t)]^2 dt} $$

For a pure sine wave, which is common, the formula for the peak-to-peak amplitude can be simplified as:

$$ V_{pp} = 2\sqrt{2} \cdot RMS \approx 2.828 \cdot RMS$$

Alternate ways of writing

That also means that

I know, this is high school level algebra, but it's been a long time and I struggled to get there. So I wrote it out in full.

So, when calculating, one then gets:

Example calculations

With wo common voltages 120V RMS and 230V RMS, we get:

And when we go back:

Given a symmetrical sine wave with the reference point as 0V, that gives also:


That was it for today. If you found this useful, I highly recommend following the course.