Title text: More generally, with great power comes great dEnergy/dt
| This explanation may be incomplete or incorrect: This explanation is very messy. Punctuation is all over the place, capitalization is very strange, and much of it is redundant, especially with the two subheadings. I'd fix it, but I don't understand anything about electricity or Ohm's law, so I'm worried I'd screw it up further.|
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This comic deliberately conflates the origin story of the comic-book superhero of Spider-Man with the origin of Ohm's law, as both the origin story of spider-man and Ohm's law deal with power, though the power is of different types.
In the origin story of Spiderman Peter Parker (who would become Spider-man) is advised by his father figure, his uncle, that "with great power comes great responsibility," where power is defined as the capacity to take action. In various versions of Spider-Man's origin story, a teenage Peter Parker is brought up by his aunt May and uncle Ben. Uncle Ben cautions Peter that "with great power comes great responsibility," referring to "power" as "capacity to take action". Through an incident involving a spider and some cutting-edge technology, Peter Parker acquires spider-like powers including great strength and the ability to adhere to walls and ceilings. Parker fails to use his new powers to stop a criminal, who then mugs and fatally shoots Uncle Ben. This failure to save his uncle haunts Parker and drives him to use his new powers for heroic purposes. Visually, this comic looks like the dying Uncle Ben counseling his nephew to use his power responsibly.
In contrast, in the xkcd comic Ohm's law is supposedly delivered to Georg Ohm by a similar authority figure in the form of relating current and resistance to power (in the unit of Watts), where power is defined as the change in energy per unit time. The unit, Ohm, is named for physicist Georg Ohm who determined experimentally that for an Ohmic resistor, the current was doubled when the electrical pressure (voltage) was also doubled.
This relationship is summarized by Ohm's law:
- Voltage = Current x Resistance (V=IR)
Electric power is defined as:
- Power = Current x Voltage (P=VI - Joule's first law)
- which, by replacing "Voltage" with "(Current x Resistance)" (from Ohm's law):
- Power = Current x (Current x Resistance) = Current² x Resistance
- which is basically the power equation alluded to in the comic.
In this case, current flowing through a resistor will dissipate power, mostly in the form of heat or light. The joke here is that given the proportionality, by definition a great (amount of) power would involve a great (amount of) current and/or resistance (squared), as here the phrase 'great power' could be taken to mean 'a large capability to do things' or 'a numerically large quantity of (electrical) power'. There is also humor in the improbability of this scenario, the comparison with Spider-man, as well as the suggestion that it was how Ohm derived his eponymous law.
The title text takes this further, by redefining the power equation as a more generalised differential equation, which simply states that power is proportional to the change of energy per unit time (dE/dt), which is another way of stating that "power = energy per unit time". In many engineering and physics books the differential form is presented as the general form from which a specific algebraic form can be derived as the differential form is more adaptable to special cases, and therefore more general, and so the title text extends the conflation of physical power and electrical power to a more generalised form.
- [A Cueball-like guy (Georg Ohm) is kneeling behind and holding his Cueball-like uncle by the shoulders as he is lying down.]
- Uncle: Remember: With great power comes great current squared times resistance.
- [Caption below the frame:]
- Ohm never forgot his dying uncle's advice.
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