Galvanometer

Galvanometer is an electrical device which is used to detect the passage of current through a circuit.

Principle

Torque acts on a current carrying coil when placed in uniform magnetic field.

τ= NIBA cos α

Construction

Galvanometer consists of:

i) A U-shaped magnet with concave shaped north and south poles.

ii) A rectangular coil C made up of enameled copper wire suspended between poles of U-shaped magnet.

iii) A non-magnetic (aluminium) frame over which the wire is wound.

iv) A suspension wire F (connected to one terminal of coil) acting as one current lead.

v) A loosely wound spiral E (connected to the other terminal of the coil) acting as second current lead.

vi) An iron cylinder D placed inside the coil to concentrate the field through it.

Working

When the current is passed through the coil, a couple (two equal and opposite forces acting on two different points on a body) act on the coil and the coil tends to rotate. Such couple is known as deflecting couple.

Deflecting torque

If N is the number of turns of the coil and A is the area then the torque due to the deflecting couple is given by

τ= NIBA cos α

Since the pole pieces of magnet are made concave to make the field radial, therefore the plane of the coil is always parallel to field, so 𝞪 = 0°

τ= NIBA cos0º

τ = NIBA (1)

τ = NIBA 𑁋 (1)

Restoring torque

As the coil turns under the action of deflecting torque, the suspension wire is twisted which gives rise to torsional couple which tends to untwist the suspension wire and restore the original position. This couple is known as restoring couple.

The torque due to restoring couple is proportional to the angle of deflection 𝚹 as long as the suspension wire obey's Hook's Law,

Thus

Restoring torque ∝ 𝚹

Restoring torque = C𝚹 𝄖 (2)

Where C is the constant of proportionality called twisting or torsional constant and it depends upon the nature of suspension wire.

Equilibrium State

When the deflecting couple balances the restoring couple then coil will come to rest. So, in equilibrium.

Deflection Torque = Restoring Torque

NIAB = C𝚹

OR, I = C𝚹 / NBA

I ∝ 𝛉 [ ∵ Since C/BAN ﹦ Constant ]

So the current passing through the coil is directly proportional to deflection.