Principle of Galvanometer:-

A moving coil galvanometer works on the principle that a current carrying coil kept in an uniform magnetic field experiences a torque.

t=NIAB sin@

(pls read @ as theta)

where

N=number of turns in the galvanometer coil
I=current flowing through the coil
A=Area of the coil
B=Magnetic Field (uniform)
@=angle btw area vector and mafnetic field


Construction of Galvanometer:-

Moving coil Galvanometer:-
In a moving coil galvanometer a coil rotates in a uniform magnetic field. Eg. Tangent Galvanometer,

1>Coil:-   
The coil is made up of insulated copper bound over a rectangular aluminum frame which is mounted over a soft iron sphere

2>Aluminum frame is used becoz:-
    i>   it is light
    ii>  it is non-magnetic
    iii>  eddy currents are produced in it which make the galvanometer dead beat i.e. make the coil to return to its original position after the current has stopped passing.

3>Phosphor bronze hair spring is used in the galvanometer which connects the galvanometer needle with the coil. Phosphor bronze is used becoz:-
    i>   it is highly elastic
    ii>   it has less elastic after effect
    iii>   it is light
    iv>   it is a good conductor
    v>    it provides least counter torque per unit deflection increasing the secsitivity of the galvanometer.

4>Cylindrical iron core:-
Soft iron has very high magnetic permeability and attracts a large number of magnetic lines of force towards itself. This increases the magnetic field on the coil and increases the torque which again results in the increased sensitivity of the galvanometer.

5>Concave shape of the magnetic poles:-
Concave shape of the magnetic poles are used to make the magnetic field radial i.e.the magnetic field is directed towards the centre i.e.towards the iron core. so @ becomes 90 and so the torque is maximum and is uniform for a constant current. This increases the sensitivity.

Working:-

When current is passed through the coil It experiences a torque t=NIAB which rotates the galvanometer needle. The Galvanometer needle becomes stationary when the torque due to the spring equals the torque due to the current. Mathematically this can be given as

c#=NIAB         (read # as phi)

where c=Torrisional Constant for the spring
          #=Galvanometer Deflection (in divisions)