Disclaimer: This is a Pokemon fanfiction; the author makes no claims of ownership of Pokemon. No profit was made in the creation or presentation of this work.
Today was another mediocre day. I often find that I have the kind of time I need to ponder some of the more mysterious aspects of the world around me. This afternoon I found myself pondering the nature of a pikachu, and asking questions that perhaps no one other than pokemon researchers and some inventors thought to ask.
For example, does a pikachu generate a regular sinusoidal voltage? I would think that at the very least one would be able to, for they can be and have been used as backup generators. It seems that the trademark red cheeks, the 'electric sacks,' are the output for whatever chemical reactions are going on inside to generate such voltage. If it's DC, which is positive and which negative? If it's AC, which is hot and which is neutral? Also, it seems that the creatures can control the voltage, since they don't electrocute everything they touch, only what they attack in battle. It must be a reasonably high voltage, too, if it can arc dozens of feet through an insulation of air. This itself is a mystery, for the bolt of electricity would strike a tree and run to ground before it would reach the target. But regardless, one could conclude that a pikachu can raise and lower the peaks of said sinusoidal voltage. Otherwise there would be arcs every which way while it was sitting around or sleeping, and that would cause obvious problems for any aspiring pikachu trainers.
Now, it is a given that a pikachu can generate voltage, whether linear or sinusoidal. There might be some kind of internal, organic switch, which can alternate between the two. A thousand volts of DC is no safer than a thousand volts of AC, except that the force of a constant DC voltage would quickly be lost as it traveled towards a rival pokemon through the resistance offered by the air. Either way, it supplies voltage, so it must also supply the current, which most likely comes from those same metabolic processes which generate voltage. The current cannot be infinite, so there must be a limit to its electrical ability, measured in ampere-hours.
The attacks will be assumed to be of linear voltage and current, to avoid some of the calculations of sinusoidal waveforms. Consider the thunder attack. Let us assume that this thunder (or lightning, actually, since thunder could hardly cause such damage) resembles natural (as in meteorological phenomena, not to imply that pikachu are unnatural) lightning. The numbers offered by various sources differ, but lightning strikes occur due to a difference in potential of somewhere between several hundred-thousand and several million volts; one million volts will be assumed. If the thunder attack lasts three seconds (as is not uncommon), then we can calculate how much energy is used. By Ohm's law the current delivered is equal to one million volts divided by the resistance of the target. Human skin has a resistance of about twenty thousand Ohms, so when Team Rocket is blasted off again, about fifty Amps are coursing through their bodies. (The ideal power dissipation, not counting that lost to the surrounding air, is fifty million Watts, but I digress.) Therefore, fifty Amps are used in those three seconds of attack. Yet there is a supply of five thunder attacks (regardless of the resistance of the target: another peculiarity. Either all pokemon have an equal resistance to draw the same amount of current from each attack, or perhaps the pikachu adapts its voltage accordingly to allow always for five attacks), and therefore that current could be sustained for fifteen seconds. Fifteen seconds is 1/240 of an hour. So, fifty Amps times 1/240 hours results in an ampere-hour rating of about two tenths. That is, a pikachu's thunder supply can deliver a constant two hundred milliamps over the course of an hour. A standard battery can have an ampere-hour rating of seventy, so the pikachu may not seem impressive, until the tremendous voltage is considered. Only short bursts of current are needed, and the high voltage is enough to cause an effectively damaging power dissipation. We can say then that a pikachu, with regard to its thunder attack, acts as a .2 Amp-hour, one million volt battery.
This may cause some contradictions, for even if a pikachu depletes its supply of thunder attacks, it still has others, such as a shock, a bolt, and a wave, and each of them always have that peculiar, limited number of uses. If all the attacks come from one repository of electrical energy, then all of the other attacks combined cannot be equal to even one thunder attack. As I am not a professional pokemon trainer myself, I couldn't say if this is in fact true, but I have heard that it isn't. If this is so, then there must be separate supplies of energy for each attack, and the pikachu lacks the ability to transport energy between them.
What can be said of a raichu? Every pokemon attack has the unique characteristic of having a set, limited supply. Or rather, this is the natural state; there are items on the market that can enlarge this supply, but let us concern ourselves only with the natural state. This constant would seem to defy common sense, since as the creature grows larger through evolution it should follow that has a larger reservoir of energy to draw from for its attacks. Yet this is not the case. If I may be allowed to be vague, only the 'strength' of the pokemon increases.
The damage dealt to a pokemon from an electric attack is due to power dissipation. (Dissipation comes in the form of heat, so one might be tempted to conclude that a fire attack and an electric attack would be equally effective, but a simple experiment with a vaporeon would disprove this; the difference in the two must be due to the manner in which the heat is delivered.) Power, of course, is equal to the product of voltage and current. Consider the following scenario. A pikachu attacks a bulbasaur, and faints the creature with three electric attacks. A raichu attacks another bulbasaur of similar, if not identical, status, and faints the creature with only one electric attack. What happened? More damage was dealt to the second bulbasaur, which must mean that either the voltage or the current was increased, possibly both. The pikachu and bulbasaur alike can be thought of as voltage sources, not current sources. Though the current does come from them, it is the result of the relationship between voltage and resistance as dictated by Ohm's law. The resistances of the bulbasaurs are the same, so the difference in power dissipation must be due to a higher voltage from the raichu.
Therefore, evolution in a pikachu yields an increased control over the nature of its voltage level, or rather, it 'raises the bar,' so to speak. It allows a higher voltage to be supplied to its electric sacks, a voltage which, perhaps, due to the internal resistance of its organic power supply, would dissipate too much heat inside the creature to guarantee its safety, or indeed, its very survival. However, virtually nothing is known about the internal anatomy of any pokemon, including pikachu. The Pokemon League has kept a ban on pokemon testing for years, and dissection is completely unheard-of.
For as much that I can deduce about pikachu, even more is left unknown, and no length of time would be long enough to allow me to figure everything out. But I don't mind. I only hypothesize. I'm no trainer; I'm not even a researcher. I'm merely a curious person who takes interest in some of the implications and applications of this 'power that's inside.'