Explanation of the root-mean-square formula for AC power

THE Amateur Radio General class license examination includes lots of stuff on alternating current, including root-mean-square voltage.

Despite looking around, I couldn’t find anything on root-mean-square voltage except that it is “the DC voltage that dissipates the same power as the AC voltage in question”. This is probably because the derivation is quite trivial, but let’s just lay it out and show just why this DC voltage is the root-mean-square.

Power can be defined as the square of the voltage divided by the resistance:

\[ P = V^2 / R \]

So the power dissipated after, say, \( \tau \) seconds is

\[ P_\tau = \int_0^\tau \frac{V^2}{R} = \frac{1}{R} \int_0^\tau V^2 \]

This makes the average power over that time period

\[ \bar{P} = \frac{1}{\tau R} \int_0^\tau V^2 \]

Create a new voltage \( V_{\text{rms}} \)to represent the DC voltage that dissipates a power \( \bar{P} \).

\[ \begin{align*}
\bar{P} = V_{\text{rms}}^2 / R &= \frac{1}{\tau R} \int_0^\tau V^2 \\
V_{\text{rms}} &= \sqrt{ \frac{1}{\tau} \int_0^\tau V^2 }
\end{align*}
\]

Observe that \( V_{\text{rms}} \) is the root of the mean of the square of \( V \).

(Using this equation, \(V_{\text{rms}} = 1/\sqrt{2}\) for \(V = \sin t\), which is where the constant of \(0.707 \) that you need to know for the license exam comes from.)

Pronunciation of “Linux”

There are three different pronunciations of Linux in use. They differ only in the first vowel—

  • /iː/ is used by Linus Torvalds himself after the pronunciation of his own name in his native Finnish
  • /ɪ/ is the standard pronunciation and the one used by the vast majority of people. This pronunciation is the natural one following English phonological rules and also reflect’s the Linux kernel’s inspiration in MINIX.
  • /aɪ/ is used by some people, notably Bruce Perens, although people who use /ɪ/ will often see it as wrong. I just realized that this reflects Linus’s first name in English.

Linguistics field notes: a failure to follow the Gricean Maxims

THIS Reddit post exemplifies the maxims of Grice’s cooperative principle, by showing the absolute mayhem that occurs when they are not followed.

In this case, OP has failed to state just what the picture shows—the title gives background only, and even then arguably not enough—leading to incredible confusion. (tl;dr spoiler explanation: he and a male friend are wearing the GF’s extensions. The GF does not appear in the picture.)

In particular this reminds me of xkcd 1028, “Communication”. In particular the title-text gets it exactly right:

Anyone who says that they’re great at communicating but ‘people are bad at listening’ is confused about how communication works.