Difference between revisions of "643: Ohm"

Explain xkcd: It's 'cause you're dumb.
Jump to: navigation, search
(Added mathiness)
(Explanation: fixed links)
 
(16 intermediate revisions by 10 users not shown)
Line 8: Line 8:
  
 
==Explanation==
 
==Explanation==
This comic is a play on the concepts of power as the human capacity to take action, and power as a strictly defined physical quantity, namely the amount of energy which flows from one locus to another in a unit of time. In calculus, this is expressed as dE/dt, hence the title text declaration that with great power comes great dEnergy/dt—though strictly speaking, great power EQUALS (is identical with) great dEnergy/dt.
 
  
The uncle's advice references the comic-book superhero {{w|Spiderman}}. 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". 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 mugging; it turns out that the victim is none other than Uncle Ben, who dies from injuries sustained. 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 counselling his nephew to use his power responsibly.
+
This comic deliberately [https://en.wiktionary.org/wiki/conflate conflates] the origin story of the comic-book superhero of {{w|Spider-Man}} with the origin of {{w|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.
  
Physical energy can exist in many different forms. In electrical physics, current flowing through a resistor generates heat. The basic units are defined such that the power (in {{w|Watt}}s) converted into heat is given by the square of the electrical current flowing (in {{w|Amperes}}) multiplied by the resistance of the component (in {{w|Ohm}}s). The unit, Ohm, is named for physicist {{w|Georg Ohm}} who determined experimentally that a given resistor would pass double the current when the electrical pressure ({{w|voltage}}) was also doubled.
+
In the origin story of Spiderman {{w|Peter Parker}} (who would become Spider-man) is raised by his Aunt May and Uncle Ben. When Parker goes through various stages of teenage angst and rebellion, his {{w|Uncle Ben}} (in different situations depending on the comics and/or movie) advises him that "with great power comes great responsibility". Here, power is taken by the reader to refer to Parker's superhero powers, acquired from a bite from a radioactive spider and via various technologies Parker designs himself. It is to be noted, however, that Uncle Ben doesn't know about these powers in the origin stories and only means this as general advice.
 +
 
 +
In contrast, in this xkcd comic, Ohm's law is supposedly delivered to {{w|Georg Ohm}} by a similar authority figure in the form of relating current and resistance to power (in the unit of {{w|Watt}}s), where power is defined as the change in energy per unit time. In real life, Ohm obviously was never "advised" about the law but instead determined experimentally that current through an Ohmic resistor was proportional to the {{w|voltage}}.  
  
 
This relationship is summarized by {{w|Ohm's law}}:
 
This relationship is summarized by {{w|Ohm's law}}:
:Current = Voltage / Resistance (I=V/R)
+
:Voltage = Current x Resistance (V=IR)
:Voltage = Current x Resistance (V=IxR)
 
:Resistance = Voltage / Current (R=V/I)
 
  
 
{{w|Electric power}} is defined as:
 
{{w|Electric power}} is defined as:
:Power = Current x Voltage (P=IxV - {{w|Joule's laws|Joule's first law}})
+
:Power = Current x Voltage (P=VI - {{w|Joule heating|Joule's first law}})
:or by replacing "Voltage" with "(Current x Resistance)" (from Ohm's law):
+
:which, by replacing "Voltage" with "(Current x Resistance)" (from Ohm's law):
:Power = Current x (Current x Resistance) = Current^2 x Resistance
+
:Power = Current x (Current x Resistance) = Current² x Resistance
 +
:which leads to the power equation alluded to in the comic.
 +
 
 +
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 {{w|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.
  
 
==Transcript==
 
==Transcript==
:[Ohm is holding his uncle by the shoulders.]
+
:[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.
 
:Uncle: Remember: With great power comes great current squared times resistance.
:Narrator: Ohm never forgot his dying uncle's advice.
+
 
 +
:[Caption below the frame:]
 +
:Ohm never forgot his dying uncle's advice.
  
 
{{comic discussion}}
 
{{comic discussion}}
 +
[[Category:Comics featuring real people]]
 +
[[Category:Comics featuring Cueball]]
 +
[[Category:Multiple Cueballs]]
 
[[Category:Physics]]
 
[[Category:Physics]]
 
[[Category:Math]]
 
[[Category:Math]]

Latest revision as of 08:57, 28 December 2015

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

Explanation[edit]

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 raised by his Aunt May and Uncle Ben. When Parker goes through various stages of teenage angst and rebellion, his Uncle Ben (in different situations depending on the comics and/or movie) advises him that "with great power comes great responsibility". Here, power is taken by the reader to refer to Parker's superhero powers, acquired from a bite from a radioactive spider and via various technologies Parker designs himself. It is to be noted, however, that Uncle Ben doesn't know about these powers in the origin stories and only means this as general advice.

In contrast, in this 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. In real life, Ohm obviously was never "advised" about the law but instead determined experimentally that current through an Ohmic resistor was proportional to the voltage.

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 leads to the power equation alluded to in the comic.

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.

Transcript[edit]

[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.


comment.png add a comment! ⋅ comment.png add a topic (use sparingly)! ⋅ Icons-mini-action refresh blue.gif refresh comments!

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)