Moving Coil Galvanometer
A galvanometer is an instrument that is used to detect small currents in a circuit. 
Principle
The working of moving coil galvanometer is based on the principle that a current carrying coil placed in an external magnetic field experiences a torque.
Construction
The construction of a moving coil galvanometer is explained below

Working
The working of a moving coil galvanometer is explained below

Calculations
Consider the magnetic torque deflects the coil through an angle α. Then, in equilibrium position, we have
Deflecting Torque = Restoring Torque
NIABsinθ = Cα
Here,
 C is called torsional constant of the spring i.e. restoring torque produced on a unit angular twist (1°).
 B = Strength of Magnetic field
 I = Current flowing through the coil
 N = Number of turns in the coil
 A = Area of the coil
 θ = Angle between area vector and magnetic field
Since the magnetic field is radial, so the angle between area vector and magnetic field is always 90°. So, sinθ = sin90° = 1. Thus, we have
NIABsin90° = Cα
NIAB = Cα
α = (NAB/C)I
Here, N, A, B and C are constants. Thus,
α ∝ I
Thus, the deflection produced in the coil is directly proportional to the current flowing through it.
Consequently, the instrument can be provided with a linear scale having equal divisions to indicate equal steps in current. Now,
Here, the factor G = C/NAB is constant for a galvanometer and is called galvanometer constant or current reduction factor of the galvanometer.
Sensitivity of Galvanometer
A galvanometer is said to be sensitive if it shows large scale deflection even when a small current is passed through it or a small voltage is applied across it.
1. Current Sensitivity
 It is defined as the deflection produced in the galvanometer when a unit current flows through it.
 It is denoted by I_{s} and given as
2. Voltage Sensitivity
 It is defined as the deflection produced in the galvanometer when a unit potential difference is applied across its ends.
 It is denoted by V_{s} and given as
Relation Between Current Sensitivity and Voltage Sensitivity
Factors Affecting Sensitivity
The sensitivity of a moving coil galvanometer depends upon the following factors
 Number of turns in its coil (N)
 Magnetic Field (B)
 Area of the coil (A)
 Torsion constant (C) of the spring and suspension wire
Increasing The Sensitivity
The sensitivity of a moving coil galvanometer can be increased in the following ways
 By increasing the number of turns (N) in the coil
 By increasing the magnetic field (B)
 By increasing the area (A) of the coil
 By decreasing the value of torsion constant (C)
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