## THEORY

The galvanometer is oriented so that the plane of the coil is vertical and aligned along parallel to the horizontal component

where

*BH*of the Earth's magnetic field (i.e. parallel to the local "magnetic meridian"). When an electrical current flows through the galvanometer coil, a second magnetic field*B*is created. At the center of the coil, where the compass needle is located, the coil's field is perpendicular to the plane of the coil. The magnitude of the coil's field is:where

*I*is the current in amperes,*n*is the number of turns of the coil and*r*is the radius of the coil. These two perpendicular magnetic fields add vectorially, and the compass needle points along the direction of their resultant*BH+B*. The current in the coil causes the compass needle to rotate by an angle*θ*:From tangent law,

*B = BH*tan*θ*, i.e.OR

or

One problem with the tangent galvanometer is that its resolution degrades at both high currents and low currents. The maximum resolution is obtained when the value of

*I = K*tan*θ*, where*K*is called the Reduction Factor of the tangent galvanometer.One problem with the tangent galvanometer is that its resolution degrades at both high currents and low currents. The maximum resolution is obtained when the value of

*θ*is 45°. When the value of*θ*is close to 0° or 90°, a large percentage change in the current will only move the needle a few degrees.