# 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-

 A rectangular coil of N turns made up of fine insulated copper wire is wound on a light non-magnetic metallic aluminium frame. The coil is suspended in between the poles of a powerful magnet by means of a phosphor-bronze wire through a torsion head which is connected to terminal T1. A cylindrical soft iron core is symmetrically positioned inside the coil to increase the strength of magnetic field and to make the magnetic field radial. The magnet is bored out cylindrically so as to create a uniform radial magnetic field. A pointer and a scale is fitted where pointer points at the scale indicating the electric current.  ## Working-

The working of a moving coil galvanometer is explained below-

 The current to be measured is sent to the coil. Since the coil is carrying current and is placed in a region of magnetic field, it experiences a torque which tries to rotate the coil. As the coil rotates, the fine wire and the spring starts twisting. This develops a restoring torque in the fine wire and the spring which tries to restore their original position. More the coil rotates, more is the twist produced in the fine wire and spring and hence more is the restoring torque produced called as torsional strain. As the coil keeps rotating, restoring torque in fine wire and spring keeps increasing. A stage is reached when the magnetic torque gets balanced by the restoring torque and the coil stops rotating. At this stage, the reading pointed by the pointer is the value of current flowing in the coil.

## 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 Is 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 Vs 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)