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Why is it when someone comes into contact with an electrical supply that their body freezes up and is unable to move away from the electrical source?

Can someone explain this through a physiological perspective?

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    $\begingroup$ Your question is bit incorrect. Person undergoing electrical shock does not get frozen in place. He/she actively grips the wire and holds it with great force. Of course, this only happens if contact occurs with inside of the palm, so the closing fist can actually grab the wire. $\endgroup$ – Agent_L May 26 '15 at 12:39
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Interesting question!

An important factor here is the let-go phenomenon, which is defined as the current level in the arm that will cause the hand to involuntarily grip the current source. When the fingers are wrapped around a large cable, most adults will be able to let go with a current of less than 6 mA. At 22 mA, however, more than 99% of adults will not be able to let go.

Nearly all cases of inability to let go involve alternating current. Alternating current repetitively stimulates nerves and muscles, resulting in a tetanic (sustained) contraction that lasts as long as the contact is continued. If this leads to the subject tightening his or her grip on a conductor, the result is continued electric current flow through the person and lowered contact resistance.

Given that the current flow in the forearm stimulates both the muscles of flexion and extension, it seems surprising that one cannot let go. However, the muscles of flexion are stronger, making the person unable to voluntarily let go (similar to the fact that a crocodile's jaws can be kept shut with your bare hands, but one should better not attempt to keep them open like that...).

Direct currents below 300 mA have no let-go phenomenon, because the hand is not involuntarily clamped.

Several different outcomes may occur when a person grasps a conductor giving 10 kV AC hand-to-hand voltage. Within 10 to 100 milliseconds, muscles in the current path will strongly contract. The person may grasp the conductor more tightly. However, mostly subjects are propelled away from the contact, likely due to generalized muscle contractions.

Reference
- Fish & Geddes, J Plastic Surg (2009); 9: 407-21

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When the body comes in contact with an electrical power supply, two things can happen. If the current flow is high enough, the body heats up just like a heating resistor, and opposed to the resistor, the body can't handle the heat, thus severe burns occur after electric shock.

But if the current is low enough not to burn "the conductor" other effects are visible. The nervous system tissue has the best conductor properties from the body. More than that, it works with action potentials, which are small chemical generated currents. When an external current gets to a nervous fiber, the fiber will conduct electricity further to the efector tissue (muscle in this case).

If electric current of sufficient magnitude is conducted through a living creature (human or otherwise), its effect will be to override the tiny electrical impulses normally generated by the neurons, overloading the nervous system and preventing both reflex and volitional signals from being able to actuate muscles. Muscles triggered by an external (shock) current will involuntarily contract, and there's nothing the victim can do about it.

The result is a powerful contraction of the muscle. But the question is what muscular groups contract? Well, all that are under the influence of a nerve under electric shock. And from here comes the freeze effect, because antagonist muscular groups contract simultaneously (for example flexor and extensor, adductor and abductor muscles in the same time). The result of this forced contraction tends to move parts of the body as dictated by the muscles that are more powerful.

The forearm muscles responsible for bending fingers tend to be better developed than those muscles responsible for extending fingers, and so if both sets of muscles try to contract because of an electric current conducted through the person's arm, the "bending" muscles will win, clenching the fingers into a fist.

You can read more on All About Circuits.

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