Question

Advantage and disadvantage of galvanometer

Answer 1

A tangent galvanometer (ref.) is a strange-seeming early instrument that measures a current by comparing the magnetic field it produces in a coil with the field of the earth. If the two fields are at right angles, the tangent of the resulting field direction, as indicated by a compass, is the ratio of the two field strengths.
To operate it, you first align the current coil perpendicular to the earth field by rotating the instrument until the compass needle aligns with the plane of the coil (i.e., perpendicular to the normal to the coil plane, the normal being the direction the current-produced field will be in). Then you apply the current, measure the compass angle, take the tangent, and multiply by a scale factor that takes into account the size and number of turns of the coil, and the strength of the earth field to yield current.
As a way of measuring current, it has no advantage over the conventional galvanometer that I can see. However, one way in which it may be useful and other galvanometers are not, is that you can use it inversely to its intended use to measure the local earth magnetic field. You do the same setup, but you apply a known current instead of an unknown current. With minimal changes to the equation you can deduce earth's field strength from the deflection angle.