643: Ohm

Explain xkcd: It's 'cause you're dumb.
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More generally, with great power comes great dEnergy/dt
Title text: More generally, with great power comes great dEnergy/dt


This comic is a play on two definitions of "power": 1)the human capacity to take action, and 2)the amount of energy which flows from one locus to another in a unit of time.

The uncle's advice references the origin story of the comic-book superhero Spider-Man. In various versions of Spiderman'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 shoot 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.

The dialogue refers to "power" in the "energy per unit time". In electrical physics, current flowing through a resistor generates heat. The basic units are defined such that the power (in Watts) converted into heat is given by the square of the electrical current flowing (in Amperes) multiplied by the resistance of the component (in Ohms). The unit, Ohm, is named for physicist Georg Ohm who determined experimentally that a given resistor would pass double the current when the electrical pressure (voltage) was also doubled.

This relationship is summarized by Ohm's law:

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

Electric power is defined as:

Power = Current x Voltage (P=IxV - Joule's first law)
or by replacing "Voltage" with "(Current x Resistance)" (from Ohm's law):
Power = Current x (Current x Resistance) = Current^2 x Resistance

The title text gives the physics definition of power in another form. In calculus, this is expressed as dE/dt, hence the statement that with great power comes great dEnergy/dt - though, strictly speaking, great power EQUALS (is identical with) great dEnergy/dt.


[Ohm is holding his uncle by the shoulders.]
Uncle: Remember: With great power comes great current squared times resistance.
Narrator: Ohm never forgot his dying uncle's advice.

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"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. 06:34, 24 December 2013 (UTC)

Funnily enough, the Dutch word for "Uncle" sounds similar to "Ohm", though it is spelled differently (Oom). 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. 09:30, 26 July 2017 (UTC)