MOVING COIL GALVANOMETER

Galvanometer: 

A galvanometer is a device to detect current in a circuit. 

Principle: 

A current carrying coil placed in a magnetic field experiences a current dependent torque, which tends to rotate the coil and produces angular deflection. 

Construction:

A galvanometer consists f a rectangular coil of fine insulated copper wire wound on a light non magnetic metallic frame. The two ends of the axle of this frame are pivoted between two bearings. The motion of the coil is controlled by a pair of hair springs of phosphor bronze. The inner ends of the springs are soldered to the two ends of the coil and the outer ends are connected to the the binding screws. The springs provide the restoring torque and serve as current leads. A light aluminium pointer attached to the coil measures its deflection on a suitable scale. 

The coil is symmetrically placed between the cylindrical pole pieces of strong permanent horseshoe magnet. 

Theory and Working:

Let Ｉ = current flowing through the coil PQRS

     a, b = sides of the coil PQRS

       A  = ab = area of the coil

       θ = angle between the direction of B and normal to the plane of the coil.

       N = number of turns in the coil

Since the field is radial, the plane of the coil always remains parallel to the field B. Magnetic forces on the sides QR and SP are equal, opposite and collinear, so their resultant is zero. According to Fleming's left hand rule, the side PQ experiences a normal inward force equal to NＩbB why is the side QR experiences an equal normal out what force. The two forces on sides PQ and RS are equal and opposite. They form a couple and exert a torque given by 

τ = one of the force x perpendicular distance between them 

τ = F a sin θ = ＩbBa sin θ = ＩBA sin θ

[ ∵ ab = A]

If the rectangular loop has N turns, the torque increases N times ie.,

τ = NＩBA sin 90° = NＩBA

Here, θ = 90°, because the normal to the plane of coil remains perpendicular to the field B in all positions. 

The torque τ deflects the coil through an angle α. A restoring torque is set up in the coil due to elasticity of the springs such that

      τᵣ ∝ α   or   τᵣ = kα 

Where K is is the the torsion constant of the springs. 

Restoring Torque = Deflecting Torque

kα = NＩBA

Or  α = (NBA/k)Ｉ

Or      α ∝ Ｉ

Thus the deflection produced in the galvanometer coil is proportional to the current flowing through it. Consequently, the instrument can be provided with a scale with equal divisions along a circular scale to indicate equal steps in current. Such a scale is called linear scale.

Ｉ = (k/NBA) α = Ｉ = Gα

G = (k/NBA) is constant for a galvanometer and is called galvanometer constant for current reduction factor of the galvanometer.