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If a resistor produces/dissipates heat when a voltage drop is applied, how does Misaka survive when she uses her most powerful electrical attacks?

See this Q&A ("How much heat damage can Misaka's shocks do to a regular human at max output?") for calculations of the rate of temperature change that would occur in a human body of similar build to Misaka experiencing heat dissipation due to a maximum shock by her.

How is she not burnt to a crisp?

Note: I'm aware that for comedic effect, Misaka often electrically shocks Kuroko (in anime season 1, ep2 21:21, ep12 22:19, in season 2, ep4 3:25, ep17 16:21 and 18:43, ep19 7:21, ep22 13:46, ep23 10:54, in season 3, ep1 5:34 21:47, etc.), and Kuroko comes out of the experience fine. I shrug that off because I enjoy it for the comedic effect. But there's no comedic effect for most of Misaka's other attacks; those moments are quite serious in atmosphere, and the author of the Toaru series shows some dedication to logical/rational explanations for scifi phenomenon in their works, so I have some expectation/anticipation of more rigour to be applied outside of comedic contexts.

My theories of possible explanations for Misaka's survival

Possible Explanation My Faith in the Explanation
She has a different specific heat capacity than a normal human body, which would mean a slower rate of temperature change. I'm doubtful of this, since she seems to experience heat similarly to her peers in the anime's season 1 beach episode (season 1 ep 13 at 12:00. She does seem relatively okay in the cold (possibly due to just trying to deflect Kuroko's advances), but reacts normally to the heat).
She has greater ability to resist heat damage than a normal human, though she still experiences the sensation similar to a normal human This would explain the beach episode, but it does seem like a strange explanation to give for an electromaster. I apologize because I have little faith (having not read the manga or light-novels myself) that a confirmation or disproval of this will be found in those: I can't see such a technical detail being given casually in the story without some "perfect context".
She has a different electrical resistance than a normal human body, which would also mean a slower rate of temperature change. Or, she can control the electrical resistance of her own body. This seems like a logical and satisfying explanation to me in that electrical resistance (at least by intuition to someone with a very shallow science background) is a highly-electricity-related property (compared to specific heat and resistance to heat damage). I wouldn't even be surprised if she could canonically control the resistance of her own body- sure, it couldn't happen in real life, but the same goes for most of her abilities and it seems believably consistent with the rest.

However, it would require higher resistence to reduce the heat dissipation by reducing the electrical power if I understand the physics correctly, so I don't understand how she could retain the power of the attack while using such a technique to protect herself against heat dissipation.
Her electric shock attacks don't involve any special electrical activity inside her own body. It's shown clearly that external electric attacks against her don't work in the anime's first season in ep3 at 17:43. This wouldn't explain how she survives usage of her railgun, where the two rails which current flows between are supposedly simulated inside her own arm.

How is she still alive?

I've watched the three seasons of the anime, but haven't read the light novels or manga adaptation. Are any of the above explanations for her survival confirmed or denied in the light novels or manga adaptations? Or is there an explanation given that I haven't considered? If so, what is it?

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  • I'm not an expert of the setting but aren't esper abilities based on their personal reality? They replace actual reality with their own. Trying to apply real world science to this seems to be an exercise in futility.
    – Turamarth
    Jan 17, 2023 at 7:57
  • @Turamarth That's a good point. After all, she is immune to exterior electrical damage (s1 ep3 17:43) and highly-resistant-to or able-to-divert internal electrical damage (s2 ep23 8:16). So if I understand you correctly, your suggestion seems to lean into my "She has greater ability to resist heat damage than a normal human, though she still experiences the sensation similar to a normal human" possible explanation (or some variation of it), which I gave my thoughts on in the post: heat resistance/negation/immunity would (in my eyes) be a weird ability for an electromaster to have.
    – starball
    Jan 17, 2023 at 8:13

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The world of A Certain Magical Index and A Certain Scientific Railgun is a world where magic and science collide. As far as the science side goes, there are still wonky forces in play. Namely, esper powers come from an individual cultivating a personal reality.

Thus, this is not purely a physics question.

From the wiki:

The concept of Personal Reality is related to quantum theory. It enables its user to ignore the Uncertainty Principle, and with regards to the Schrödinger's cat thought experiment, will allow them to interfere with and distort the microscopic world using different laws.

Since I have the first few volumes of A Certain Magical Index, I can get the actual quote from the section referenced (though the wiki does a good summary, so I won't quote the whole thing). From volume 3, chapter 2, section 8:

"What we call espers are those people whose power to see the reality of this fifty percent hard candy has been shifted away from that of normal people. RSPK Syndrome--in layman's terms, some children lose the ability to perceive reality as it is because of poltergeists, or via trauma or excessive stress. Also, the Gantzfeldt Experiment used in Ability Development purposely shuts down your five senses and essentially cuts you off from normal reality.[...] An 'esper' who has been cut off from the usual reality can acquire a personal reality that differs from the rest of us. As a result, they alter the microscopic world using laws different from regular people.... They can acquire 'powers' like breaking things without touching them or seeing the future a year from now just by closing their eyes. [...] The 'Mnemonics' we carry out refers to artificially creating one of these personal realities. To put it more simply, we help cause certain kinds of disorders in their brains by using things like medicine and suggestion."

A personal reality might be called a delusion that becomes real, precisely because one believes it is real. Misaka's powers exist in her own personal reality. Thus, she does not need to comply to the physics of the real world. It doesn't make sense that her powers would incinerate her in her own personal reality, in her own delusion.

The magic/religion side can't be discounted either, just because we're talking about the science side. For instance, continuing in the dialogue I quoted, we get this from Miss Komoe:

"[System] refers to one who arrives at heaven's intent in an ungodly body. Our objective is to see what lies beyond Level Five, after all. We humans don't understand the truth of the universe. So it's simple. If there were someone with a status above human, they should obviously be able to understand god's answer."

Additionally, the entire world of A Certain Magical Index has multiple layers of reality, so it's not just personal realities that distort laws of the world. See https://toarumajutsunoindex.fandom.com/wiki/Phase for details (spoilers). From the wiki:

The many religions (Christian, Buddhist, Celtic, Indian, Shinto, Incan, Aztec, Greek, Roman, Norse etc) which have arisen throughout history have had the effect of applying various phases to the world. The world is said to contain as many phases are there are divine legends and religions. Extremely powerful beings, such as Magic Gods, are also capable of applying new phases and manipulating existing ones.

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    The details of personal reality seem to not be touched upon as much in the anime (I haven't read the light-novels or manga adaptation), and I haven't watched much of the Index anime so I didn't know about this! Thanks.
    – starball
    Jan 18, 2023 at 0:00

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