It is an instrument used to detect small currents using tangent law by keeping the magnetic needle at equilibrium under the torques of the Bcoil & BH.
The plane of the coil is set parallel to the magnetic meridian such that the magnetic needle points 0– 0 position. Now current to be measured is passed in the coil. The magnetic field produced by this current acts at right angles to the plane of the coil. Torque due to this field deflects the needle while the torque due to BH tends to restore the needle till the equilibrium is achieved. Let in equilibrium the magnetic needle makes an angle θ with the horizontal component of earth’s magnetic field, then we can write
Bcoil = BH tanθ
or I = k tanθ
Here is called reduction factor.
It is the amount of current required to produce a deflection of 450 in the magnetic needle. A tangent galvanometer is said to be both sensitive & accurate, if the change in its deflection is large for a given fractional change in current. The percentage error in the measurement of current is minimum when the deflection is 450.