A galvanometer is a device used to detect feeble electric currents in a circuit. It consists of a coil suspended between the poles of a powerful magnet. As current passes through the coil, it deflects. It can be detected from the deflection on galvanometer needle. The deflection is proportional to the current passed through it. Its working is based on the principle that a coil placed in a uniform magnetic field experiences a torque when an electric current is set up in it. The deflection of the coil is determined by a pointer attached to it, moving on the scale. When a coil carrying current I is placed in a radial magnetic field, the coil experiences a deflection θ which is related to I as I = kθ, where k is a constant of proportionality and is termed as figure of merit of the galvanometer.
This video explains how to determine the resistance of a galvanometer by half deflection method and to find its figure of merit.