k C' = H tan x'
hence
C: C' = tan x : tan x'
This means that the currents passing through the coil of a tangent galvanometer are proportional, not to the angle of deflection, but to the tangent of that angle.
Fig. 519.--Diagram illustrating the tangent law. This is the law of the combined action of two magnetic fields upon a magnetic needle. If two magnetic fields be at right angles in direction as indicated in the figure, the resultant field is obtained by the parallelogram of forces and it makes an angle θ with one of the component fields such that tan θ = M + H where M and H are the strengths of the component fields. In the tangent galvanometer this principle is employed in the measurement of currents. A magnetic needle is pivoted in a field of known strength. The current to be measured is passed round a coil (or coils) which generates a field at right angles to the original field. The needle then lies along the direction of the resultant field, and by finding the tangent of its angle of deflection, and knowing the field strength produced by unit current in the coil, the current strength can be found.
Fig. 520.--Graduation of tangent galvanometer scale with divisions representing tangent values. In the figure let a tangent OT be drawn to the circle, and along this line let any number of equal divisions be set off, beginning at O. From these points draw lines back to the center. The circle will thus be divided into a number of spaces, of which those near O are nearly equal, but which get smaller and smaller as they recede from O. These unequal spaces correspond to equal increments of the tangent. If the scale were divided thus, the readings would be proportional to the tangents.
Ques. Upon what does the sensibility of a tangent galvanometer depend?
Ans. It is directly proportional to the number of turns of the coil and inversely proportional to the diameter of the coil.