Difference between revisions of "643: Ohm"

Explain xkcd: It's 'cause you're dumb.
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{{comic
 
{{comic
 
| number    = 643
 
| number    = 643
| date      =  
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| date      = September 30, 2009
 
| title    = Ohm
 
| title    = Ohm
 
| image    = ohm.png
 
| image    = ohm.png
Line 8: Line 8:
  
 
==Explanation==
 
==Explanation==
This cartoon 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 tooltip declaration that with great power comes great dEnergy/dt - though strictly speaking, great power EQUALS (is identical with) great dEnergy/dt.
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This comic is a play on two definitions of "power":
 +
#The human capacity to take action, and
 +
#The amount of energy which flows from one locus to another in a unit of time.
  
The saying references the comic-book superhero Spiderman. In various versions of Spiderman's origin story, teenager Peter Parker is being 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, the xkcd cartoon 643 recalls the dying Uncle Ben counselling his nephew to use his power responsibly.
+
The uncle's advice references the origin story of the comic-book superhero {{w|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.
  
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 Watts) converted into heat is given by the square of the electrical current flowing (in Amperes) multiplied by the reistance 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.
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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 {{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 (within a reasonable range of values) a given resistor would pass double the current when the electrical pressure ({{w|voltage}}) was also doubled.
  
The main cartoon text is therefore simply a statement that in electrical physics, when current flows through a resistor, the power dissipated is equal to the current squared, multiplied by the resistance.
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This relationship is summarized by {{w|Ohm's law}}:
 +
:Current = Voltage / Resistance (I=V/R)
 +
:Voltage = Current x Resistance (V=IR)
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:Resistance = Voltage / Current (R=V/I)
 +
 
 +
{{w|Electric power}} is defined as:
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:Power = Current x Voltage (P=IV - {{w|Joule heating|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
 +
 
 +
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. This {{w|differential equation}} describes the change of energy by time.
  
 
==Transcript==
 
==Transcript==
<!-- The transcript can be found in a hidden <div> element on the xkcd comic's html source, with id "transcript".
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:[Ohm is holding his uncle by the shoulders.]
  -- Tip: Use colons (:) in the beginning of lines to preserve the original line breaks.  
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:Uncle: Remember: With great power comes great current squared times resistance.
  -- Any actions or descriptive lines in [[double brackets]] should be reduced to [single brackets] to avoid wikilinking
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:Ohm never forgot his dying uncle's advice.
  -- Do not include the title text again here -->
 
  
{{comic discussion}}  
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{{comic discussion}}
<!-- Include any categories below this line-->
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[[Category:Physics]]
 +
[[Category:Math]]

Revision as of 04:30, 21 November 2014

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

Explanation

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 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.

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 (within a reasonable range of values) 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=IR)
Resistance = Voltage / Current (R=V/I)

Electric 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

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. This differential equation describes the change of energy by time.

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)