Humboldt State University ® Department of Chemistry

Robert A. Paselk Scientific Instrument Museum

From : Kimball, Arthur Lalane, A College Text-Book of Physics, 3rd ed., H. Holt and Co., New York (1923) pp.468-9.
© Copyright 1998 R. Paselk

688. Measurement of Current. - The strength of an electric current may be measured by its magnetic effect or by its heating or chemical action. Instruments which measure a current by its action on a magnetic needle are known as galvanometers.
389. Tangent Galvanometer. - In the tangent galvanometer there is a circular coil having one or more turns of wire, at the center of which a magnetic needle is either balanced on a point or suspended by a fine fiber of silk or quartz. The instrument is placed so that the plane of the coil is vertical and in the magnetic north and south plane. When a current is sent through the coil the needle turns to one side or the other, and the strength of the current is proportional to the tangent of the angle of deflection, as may be shown as follows:
The force due to the current in the coil is at right angles to the plane of the coil at its center and the strength of the field at that point in a given coil is proportional to the strength of the current. Let G represent the strength of field at the center due to the coil when unit current is flowing, then IG will be the strength of field when the current strength is I. Let OA in figure 397 represent the plane of the coil and O the point where the needle is placed, then when no current is flowing the needle points in the direction OA, being acted on only by the horizontal component H of the earth's magnetic force. The magnetic force F due to the current in the coil is IG and at right angles to H, therefore, the resultant force R is the diagonal of the rectangle whose sides are IG and H, and
where x is the angle which the resultant force makes with H. But the needle must point in the direction of the resultant force, and so x is the angle through which the needle turns. Therefore
and if H and G are known the current may be determined by measuring the angle x.
690. Coil Constant of a Tangent Galvanometer. - In case of a tangent galvanometer the magnetic force F due to the coil is expressed by IG.
But if the current is measured in electromagnetic units,
And since the length of n turns of wire of radius r is ,
The galvanometer coil constant G can be calculated from this formula when the coil of the galvanometer has so large a radius compared with the length of the needle that the poles of the needle may be regarded as at the center, and when the cross section of the coil is so small that all the turns bear ncarly the same relation to the needle.
If G is determined in this way, r being measured in centimeters, and if H is found by the method described in [section]498, the current will be found in C. G. S. electromagnetic units by the use of the formula .
To obtain the current strength in amperes, we must take as the value of the coil constant
By this method the strength of a current is determined in amperes directly from the fundamental units of length, mass, and time, for we have already seen how the measurement of H is based on these units. A tangent galvanometer in which the constant is determined in this way directly from measurements of the coil is known as a standard galvanometer.

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