Moving coil Galvanometer: A galvanometer is a device used to detect current in a circuit.

Principle: If a current carrying coil placed in a magnetic field experiences a torque, the magnitude of which depends on the strength of current.

Theory and working:

In fig:, we have

l = current flowing through the coil PQRS

a, b = sides of the rectangular coil PQRS

A = ab = area of the coil

N = number of turns in the coil

The two forces on sides PS and QR are equal and opposite.

They form a couple and exerts a torque given by

τ = force * perpendicular distance

= NIbB * a sin 90 = NIB (ab) = NIBA

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

τ_restoring ∝ α 

or τ_restoring = K α

Where k is torsion constant of the spring i.e. torque required to produce unit angular twist. In equilibrium position,

Restoring torque = Deflecting torque

k α = NIBA

α = (NBA/k)*I

α ∝ I

Thus the deflection produced in the galvanometer coil is proportional to the current flowing through it. Also,

I = (k/NBA)* α = Gα

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

Figure of merit of a galvanometer: It is defined as the current which produces a deflection of one scale division in the galvanometer and is given by

G = I/α = k/NBA

Sensitivity of a 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.

Current sensitivity: It is defined as the deflection produced in the galvanometer when a unit current flows through it.

Current sensitivity, I_s = α/I = NBA/k

Voltage sensitivity: It is defined as the deflection produced in the galvanometer when a unit potential difference is applied across its ends.

Voltage sensitivity, V_s = α/v = NBA/kR

Factors on which the sensitivity of a moving coil galvanometer depends:

1. Number of turns N in the coils.

2. Magnetic field B.

3. Area A of the coil.

4. Torsion constant k of the spring and suspension wire.

Factors on which the sensitivity of a moving coil galvanometer can be increased:

1. By increasing the number of turns N of the coil.

2. By increasing the magnetic field B.

3. By increasing the area A of the coil.

4. By decreasing the value of torsion constant.

Conversion of a galvanometer into an ammeter:

An ammeter is a device used to measure current through a circuit is connected in series in a circuit having very small resistance. An ideal ammeter should have zero resistance.

To convert a galvanometer in to ammeter, a small resistance called shunt is connected in parallel with the galvanometer coil.

Let G be the resistance of the galvanometer,

l­_g – the current with which galvanometer gives full scale deflection

0 – l the required current range of the ammeter

S – shunt resistance

l – l_g – current through the shunt

P.D. across the galvanometer = P.D. across the shunt

l_g G = (l – l_g)S

S = (I_g/I - I_g)*G

I_g = (S/G – S)*I

Conversion of a galvanometer into a voltmeter:

A voltmeter is a device for measuring potential difference across any two points in a circuit. It is connected in parallel with the circuit element across which the potential difference is intended to be measured. Voltmeter should have high resistance. An idea voltmeter should have infinite resistance.

A galvanometer can be concerted into a voltmeter by connecting a high resistance in series with it.

Let G be the resistance of the galvanometer,

l_g – the current with which galvanometer gives full scale deflection

0-V the required range of the voltmeter

R – the high series resistance

Total resistance = R+G

By ohm’s law,

I_g = V/R+G

R+G = V/I_g

R = (V/I_g)-G

Advantages of moving coil galvanometer:

1. A moving coil galvanometer can be made highly sensitive y increasing N,B,A and decreasing k.

2. As the coil is wound over a metallic frame, the eddy currents produced in the frame bring the coil to rest quickly

Disadvantages of a moving coil galvanometer:

1. Its sensitiveness cannot be changed at will.

2. All types of the galvanometer coil galvanometer are easily damaged by overloading.