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- From : Kimball, Arthur Lalane, A College Text-Book
of Physics, 3rd ed., H. Holt and Co., New York (1923) pp.468-9.
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- © Copyright 1998 R. Paselk
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- 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.
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- 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:
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- 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
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- 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.
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- 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.
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- 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
.
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- 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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- © R. Paselk
- Last modified 22 July 2000
