The Relationship between Voltage and Energy

Energy is proportional to voltage squared. If we make the assumption that a variable voltage is being fed to a constant load-resistor, then with voltage, current would increase, and current would get multiplied by voltage again, to result in energy.

Sound energy is proportional to sound pressure squared. With increasing sound pressure, minute displacement / compression of air results, which causes displacement to rise, and displacement times pressure is again – energy.

The decibel scale is in energy units, not pressure units. Therefore, if a voltage increases by the square root of two, and if that voltage is fed to a constant load, then energy doubles, which is loosely expressed as a 3db relationship. A doubling of voltages would result in a quadrupling of energy units, which is loosely described as a 6db relationship.

Something similar happens to digitally sampled sound. The amplitudes of the samples correspond roughly to the Statistical concept of Standard Deviation, while the Statistical concept of Variance, corresponds to signal-energy. Variance equals Standard Deviation squared…

Dirk

I should add that this applies to small-signal processing, but not to industrial power-transmission. In the latter case, the load resistances are intentionally made to scale with voltages, because the efficiency-gains that stem from voltage-increases, only stem from keeping current-levels under control. Thus, in the latter case, higher amounts of power are transmitted, but without involving higher levels of current. And so here, voltages tend to relate to power units more-or-less linearly.

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The wording ‘Light Values’ can play tricks on people.

What I wrote before, was that between (n) real, 2D photos, 1 light-value can be sampled.

Some people might infer that I meant, always to use the brightness value. But this would actually be wrong. I am assuming that color footage is being used.

And if I wanted to compare pixel-colors, to determine best-fit geometry, I would most want to go by a single hue-value.

If the color being mapped averages to ‘yellow’ – which facial colors do – then hue would be best-defined as ‘the difference between the Red and Green channels’.

But the way this works out negatively, is in the fact that actual photographic film which was used around 1977, differentiated most poorly between between Red and Green, as did any chroma / video signal. And Peter Cushing was being filmed in 1977, so that our reconstruction of him might appear in today’s movies.

So then an alternative might be, ‘Normalize all the pixels to have the same luminance, and then pick whichever primary channel that the source was best-able to resolve into minute details, on a physical level.’

Maybe 1977 photographic projector-emulsions differentiated the Red primary channel best?

Further, given that there are 3 primary colors in most forms of graphics digitization, and that I would remove the overall luminance, it would follow that maybe 2 actual remaining color channels could be used, the variance of each computed separately, and the variances added?

In general, it is Mathematically safer to add Variances, than it would be to add Deviations, where Variance corresponds to Deviation squared, and where Variance therefore also corresponds to Energy, if Deviation corresponded to Potential. It is more generally agreed that Energy and its homologues are conserved quantities.

Dirk