Moving Coil Galvanometer

What is a Moving Coil Galvanometer?

It is an instrument used for the detection and measurement of small electric currents.

Principle of Moving Coil Galvanometer:

When a current-carrying conductor is placed in a magnetic field, it experiences a torque which is given by-

𝜏 = nIBA Cosθ

Construction of Moving Coil Galvanometer:

A rectangular or circular coil PQRS is made by winding a large number of turns of fine insulated copper wire on a light, non-magnetic metallic frame. It is suspended by a very thin phosphor-bronze fibre (W) from a torsion head (H), which is connected to a terminal screw (T1). One need of the coil wire is connected to T. A small circular mirror (M) is attached vertically to the suspension wire. The other end of the coil wire is taken at the lower side which is connected to a fine, loosely wound spring (K). The other end of the spring is connected to another terminal screw (T2). The coil is made to hang in the space containing a powerful magnetic field. In fact, the coil is positioned between the pole pieces of a permanent horseshoe magnet (N, S). The surfaces of the two-pole pieces are made concave cylindrical and in between them, inside the coil, a cylindrical piece of soft iron is fixed which is called ‘core’ (L). The coil is hanged in such a way that it may not touch the core at normal or in any rotated position. The whole arrangement is enclosed in a non-magnetic box with a glass panel at the front side. Three levelling screws are provided at the base of the box.

Note- L is a soft-iron core, which may be spherical if the core is circular and it is cylindrical if the coil is rectangular. This makes the magnetic field linked with the coil to be radial field i.e. θ = 0°.

moving coil galvanometer construction - Moving Coil Galvanometer

Theory of Moving Coil Galvanometer:

Suppose the coil PQRS, is suspended freely in the magnetic field. Let ‘l’ be the length of the coil, ‘b’ be the breadth of the coil, ‘n’ be the number of turns in the coil and ‘I’ be the current flowing through the coil. Also, let ‘B’ be the magnetic field produced by the pole pieces N and S.

Now, the torque acting on the coil PQRS, carrying current I, placed in magnetic field B is given by-

𝜏 = nIBA Cosθ
In the case of radial filed, θ = 0°
𝜏 = nIBA . Cos0°
𝜏 = nIBA

Due to this torque, the coil deflects. Hence it is also called deflecting torque.

Deflecting Torque = nIBA ……………(a)

Due to hair spring, a restoring Torque also acts on the coil, mathematically,

Restoring Torque = K . θ ……………(b)

Where K= Torque per unit deflection

θ = Deflection produced in the coil

At Equilibrium, Deflecting Torque = Restoring Torque

nIBA = K . θ
I = K/nBA . θ …………..(c)
Put K/nBA = G = Galvanometer Constant
I = G . θ
I ∝ θ

Thus current flowing through the Galvanometer is directly proportional to deflection produced in the coil.

Current Sensitivity:

It is defined as the deflection produced in the galvanometer when a unit current flows through it. It is denoted by IS. If ‘θ’ be the deflection produced in the Galvanometer, when current ‘I’ passes through it, then

IS = θ/I = nBA/K [ From (c), θ/I = nBA/K]

The S.I.unit of IS is radian/ampere.

Voltage Sensitivity:

It is defined as the deflection produced in the galvanometer when a unit voltage is applied across the two terminals of a galvanometer. It is denoted by VS. If ‘V’ be the voltage applied across the terminals of the galvanometer and ‘θ’ be the deflection produced in the galvanometer, then

VS = θ/V = θ/IR = nBA/KR [Where V = IR; θ/I = nBA/K]

The unit of voltage sensitivity is radian/volt.

Conditions for Sensitive Galvanometer:

A Galvanometer is said to be very sensitive if it shows large deflection even when a small current is passed through it.

From theory of Galvanometer, From (c),

θ = nBA/K . I

Thus ‘θ’ will be large, if

  • n is large
  • B is large
  • A is large
  • K is small

(1) We cannot increase the value of ‘n’ beyond a certain limit, because it makes the galvanometer bulky.

(2) We can increase the value of ‘B’ by using a strong horse-shoe magnet.

(3) We cannot increase the value of ‘A’ beyond a certain limit, because it makes the galvanometer bulky and unmanageable.

(4) We can decrease the value of ‘K’. We know the value of ‘K’ is very small for phosphor-bronze or for quartz. That is why in sensitive galvanometer, a phosphor-bronze strip is used.


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