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