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The motivation for my question is understanding how electricity gets through your skin as opposed to running along it, and how the presence of things like water on the skin affect the relative deadliness of electricity, or ability of it to permeate the skin.

I don't understand how to view the body as a resistor, as the skin, and all the components of the body have different resistances and thicknesses. How do I know what parts of the body carry significant current? And how much current in total?

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One of the prerequisites for understanding exactly how an electric current "screws up your heart beat" is, I think, an exact understanding of the electrical nature of the heart muscle. I'm thinking that is beyond the scope of this site. –  Alfred Centauri Jun 10 '13 at 23:25
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You might want to check out this biology.stackexchange.com/q/4959 though admittedly the one answer is lacking in detail. It helps if you already understand how electrical signaling occurs in animals. Besides stopping your heart, there is also just raw cell damage: biology.stackexchange.com/q/960 –  Chris White Jun 10 '13 at 23:28
    
As this stands there are far too many questions here. There are straight forward but mathematically intensive ways to treat heterogeneous resisters, and they follow directly from the usual parallel and series rules, though it helps to think in terms of conductivity and potential. –  dmckee Jun 12 '13 at 2:56
    
OK. I've taken a crack at making the underling physics the center of attention here. However as I don't know your level of math preparation I'm unsure how much the answers will help you. –  dmckee Jun 12 '13 at 3:10
    
As incapable as I sound, I'm fairly decent at understanding-Now all I need is an answer! Thank you dmckee! –  Anthony Jun 12 '13 at 5:49
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2 Answers

Firstly, let us construct a proper model for your purpose. The skin has a very high resistance(on the order of hundreds of kilo ohms) when it is dry. However, when the skin is wet, salt on your skin is dissolved and along with water, fills the pores in your skin, creating a highly conductive path (on the order of hundreds of ohms, thanks to conductivity due to ions present in the water) through the skin. But beneath your skin, there are all sorts of conductive materials filled with ions, especially your blood.

Now, the way body works as a conductor will vary depending on how it is being shocked. If we are inspecting a microshock, for example if a catheter inserted into the heart is not grounded properly and is at a nonzero voltage, then, if the patient touches the chassis of a grounded electronic device, the path of conduction will be:

Catheter - Blood - Heart - Rest of internal structure(mostly blood) - Skin - Chassis

Now in this case, most of the resistance comes from the skin interface (Order of 10 - 100 ohms from inside the body vs. Order of 100 kohm's from the skin). However, In the case of a microshock, a few micro amperes are enough to cause the heart to enter into a state of fibrillation, killing the patient in a matter of seconds, since all of the current flows through heart.

However, if the shock is a macroshock, both sources are located outside of the body. In this case, the current will have to penetrate the skin twice, in a manner as follows:

Source 1 - Skin - Blood & Tissues - Skin - Source 2

Again, the skin causes most of the resistance, and this time there are 2 skin interfaces, causing half as large current as a microshock. However, the major difference now is that the current is distributed throughout the entire body instead of being focused on a crucial organ, therefore an order of hundred milliamps may be necessary to cause any life threatening damage.

Summary:

  • You may treat the skin as the only source of resistance in most cases(if the skin is dry).

  • The life threatening aspect of electricity is more related to how the shock is applied as opposed to the magnitude of the current. There are lightning strike survivors, yet people die to microshocks every now and then.

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Also, in the case of a macroshock, forming the conduction path from one hand to the other will be deadlier than forming the conduction path from a hand to a foot, since the conduction path will not involve heart, and will require a very large amount of current to cause it to go into fibrillation. This is how most people survive lightning strikes. –  Cem Oct 22 '13 at 18:12
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There have been attempts to model the body and study what happens during discharges, like from a taser. Finite Element Models (FEM) for testing human body are pretty accurate. Here's an example of current density distribution due to a shock to the skin and how the current flows.

current flow

Where the physician's report described the body's response to current flow:

Current decreases rapidly with distance from electrode. The fat and skeletal muscle layers have an electric shell effect on currents that reach into deeper tissue layers (such as the heart): -The fat layer attenuates the electric field by at least 25 times, even under worst-case minimal thickness assumptions -Skeletal muscle preferred longitudinal (with the grain) electrical conduction diverts about 88% of the current away from deeper tissue layers

In the muscle layer: -the transverse current density is less than 15 mA/cm -the equivalent field strength is in the 15-30 V/cm range: greater than 2.25 V/cm – threshold to capture motor neurons but much low lower than levels required for irreversible electroporation (1600 V/cm – Gehl et al. 1999

The fat and skeletal muscle layers significantly reduces the current that reaches deeper into the body. The skin-heart minimal distance for typical in-custody suspects is at least two times greater than the maximum distance estimated by theoretical models as being necessary to induce VF [ventricular fibrillation]

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