To begin with, we often hear the question asked--why is it that certain wires carrying very large currents give very little shock, whereas others, with very small currents, may prove fatal to those coming in contact with them? The answer to this is--that the shock a person experiences does not depend upon the current flowing in the wires, but upon the current diverted from them and flowing through the body.
The muscular contraction due to a galvanic current, which was first observed in the frog, gives a good illustration of the fact that it requires only a very minute current to flow through the muscles in order to contract them. Thus the simple contact of pieces of zinc and copper with the nerves generated current sufficient to excite the muscles--a current which would require a delicate galvanometer for its detection. What is true of the muscles of the frog holds good also for the human muscles; they too are very susceptible to the passage of a current.
In order to determine the current which proves fatal we need only to apply the formula which expresses Ohm's law, viz., C=E/R, or the current (ampere) equals the electromotive force (volt) divided by the resistance (ohm).
According to the committee of Parliament investigation, the electromotive force dangerous to life is about 300 volts; this then is the quantity, E, in the formula. There remains now only to determine the resistance in ohms which the body offers to the passage of the current. In order to obtain this, a series of measurements under different conditions were made. On account of the nature of the experiment a high resistance Thomson reflecting galvanometer was used, with the following results.
When the hands had been wiped perfectly dry, the resistance of the body was about 30,000 ohms; with the hands perspiring ordinarily it fell to 10,000 ohms; whereas when they were dripping wet it was as low as 7,000 ohms. Our readers can judge this resistance best when we state that the Atlantic cable offers a resistance of 8,000 ohms.
Taking an ordinary condition of the body, with the hands perspiring as usual, we would have the resistance equal to 10,000 ohms. Applying the two known quantities in the formula, we get:
C = (300 / 10,000) - (1 / 33.333+)
This means, therefore, that when the electromotive force or potential is great enough to send a current of 1/33 ampere through the body, fatal results will ensue. This current is so minute that it would deposit only about 6 grains of copper in one hour, a grain being 1/7,000 of a pound.
Let us now compare these figures with some actual cases, taking as an example a system of incandescent lighting. In these systems the difference of potential between any two points of the circuit outside of the lamps does not exceed 150 volts. Taking this figure, therefore, it will be seen that under no circumstances can the shock received from touching these wires become dangerous--not even by touching the terminals of the dynamo itself; because in neither case can a current be driven through the body, sufficient to cause an excessive contraction of the muscles.
In a system of arc lighting, however, we have to deal with entirely different conditions; for, while in the incandescent system the adding of a lamp, which diminishes the resistance, requires no increase of electromotive force, the contrary is the case in the arc light system. Here every additional lamp added to the circuit means an increase in resistance, and consequent increase in electromotive force or potential. Taking for example a well known system of arc lighting, we find that the lamps require individually an electromotive force of 40 volts with a current of 10 amperes. In other words, the difference in potential at the two terminals of every such lamp is 40 volts. Consequently, if the circuit were touched in two places, including between them only one lamp, no injurious effects would ensue. If we touch the circuit so as to include two lamps between us, the effect would be greater, since the potential between those two points is 2 x 40 volts. We might continue in this manner touching the circuit until we had included about 7 or 8 lamps, when the shock would become fatal, since the point would be reached at which the difference of potential is great enough to send a dangerous current through the body.