A

A tangent galvanometer works on the principle of the tangent law of magnetism, which states that the current $I$ passing through the coil is directly proportional to the tangent of the angle of deflection $\theta$.

The mathematical equation for a tangent galvanometer is given by:
$$I = K \tan \theta$$

Where:

• $I$ is the electric current flowing through the galvanometer coil (measured in Ampere).
• $\theta$ is the angle of deflection of the magnetic needle (measured in degrees or radians).
• $K$ is the reduction factor of the tangent galvanometer.

Since $\tan \theta$ is a dimensionless trigonometric ratio, the unit of the reduction factor $K$ must be identical to the unit of electric current $I$.

Therefore, the SI unit of the reduction factor of a tangent galvanometer is Ampere.

Hence, the correct option is A.