643: Ohm

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Ohm

Title text: More generally, with great power comes great dEnergy/dt

Explanation

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 Spider-man 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. Not following this advice later leads to his Uncle's death. In contrast, in the XKCD comic Ohm's law is delivered to Georg Ohm in the form of relating current and resistance to power in the unit of (in Watts), where power is defined as energy per unit time.

The humor lies in the improbability of this scenario, the comparison with Spider-man, as well as the play on the different definitions of power

The title text defines power in terms of a simple differential equation. Read literally it says that with great power comes a great absorption of energy (dE) per unit time (1/dt), but taken as a definition it says that "power = energy per unit time". In many engineering and physics books the equations are provided in algebraic form as well as differential form as the differential form is more adaptable to special cases, and therefore more general.

Spiderman

The uncle's advice references the origin story of the comic-book superhero Spider-Man. 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 — 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.

Georg Ohm and Ohm's Law

The unit, Ohm, is named for physicist Georg Ohm who determined experimentally that (within a reasonable range of values) a given resistor would pass double the current when the electrical pressure (voltage) was also doubled. Current flowing through a resistor dissipates power, mostly in the form of heat or light.

This relationship is summarized by Ohm's law:

Current = Voltage / Resistance (I=V/R)

Voltage = Current x Resistance (V=IR)

Resistance = Voltage / Current (R=V/I)

Atomic power is defined as:

Power = Current x Voltage (P=IV - Joule's first law)

or by replacing "Voltage" with "(Current x Resistance)" (from Ohm's law):

Power = Current x (Current x Resistance) = Current² x Resistance

Transcript

[Ohm is holding his uncle by the shoulders.]

Uncle: Remember: With great power comes great current squared times resistance.

Ohm never forgot his dying uncle's advice.

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Discussion

"who determined that a given resistor would pass double the current..." -Actually, this is true only of ohmic resistors, which have constant resistance. Wire resistors, which I'm assuming are what Ohm used, are essentially ohmic for low voltage/current, but their resistance increases at high voltage because they give off dramatically more energy as heat. Other types of resistors have different behaviour. For example, semiconductors have low resistance in one direction and high resistance in the other. Probably someone should correct this! Sciepsilon (talk) 01:51, 1 December 2013 (UTC)

Somebody really should not. 108.162.219.223 06:34, 24 December 2013 (UTC)

Funnily enough, the Dutch word for "Uncle" sounds similar to "Ohm", though it is spelled differently (Oom). 162.158.111.229 11:02, 6 May 2017 (UTC)

"... both the origin story of spider-man and Ohm's law deal with power". No, Ohm's law doesn't mention power at all. 108.162.250.29 09:30, 26 July 2017 (UTC)