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