JEE Main & Advanced Physics Magnetism Tangent Galvanometer

It consists of three circular coils of insulated copper wire wound on a vertical circular frame made of nonmagnetic material as ebonite or wood. A small magnetic compass needle is pivoted at the centre of the vertical circular frame. When the coil of the tangent galvanometer is kept in magnetic meridian and current passes through any of the coil then the needle at the centre gets deflected and comes to an equilibrium position under the action of two perpendicular field : one due to horizontal component of earth and the other due to field (B) set up by the coil due to current.

In equilibrium \[B={{B}_{H}}tan\theta \] where \[B=\frac{{{\mu }_{0}}ni}{2r}\]; n = number of turns, r = radius of coil, i = the current to be measured, \[\theta =\] angle made by needle from the direction of \[{{B}_{H}}\] in equilibrium.

Hence \[\frac{{{\mu }_{0}}Ni}{2r}={{B}_{H}}\tan \theta \]  \[\Rightarrow \] \[i=k\tan \theta \] where \[k=\frac{2r{{B}_{H}}}{{{\mu }_{0}}N}\] is called reduction factor.