# The Moving Coil Galvanometer

Have you ever wondered how the utility company knows how much power you use each month? In short, it uses an electric meter. The galvanometer is an instrument used to determine the presence, direction, and the strength of an electric current in a conductor.

When an electric current is passing through the conductor, the magnetic needle tends to turn at right angles to the conductor so that its direction is parallel to the lines of induction around the conductor and its north pole points in the direction in which these lines of induction flow. A galvanometer is a type of ammeter. It is an instrument for detecting and measuring electric current.

## Moving Coil Galvanometer

Moving coil galvanometer is an electromagnetic device that can measure small values of current. It consists of permanent horseshoe magnets, coil, soft iron core, pivoted spring, non-metallic frame, scale, and pointer.

### Principle of Moving Coil Galvanometer

Torque acts on a current-carrying coil suspended in the uniform magnetic field. Due to this, the coil rotates. Hence, the deflection in the coil of a moving coil galvanometer is directly proportional to the current flowing in the coil.

[source: Redefining The Knowledge]

The Moving Coil Galvanometer

### Construction of Moving Coil Galvanometer

It consists of a rectangular coil of a large number of turns of thinly insulated copper wire wound over a light metallic frame. The coil is suspended between the pole pieces of a horseshoe magnet by a fine phosphor – bronze strip from a movable torsion head. The lower end of the coil is connected to a hairspring of phosphor bronze having only a few turns.

The other end of the spring is connected to a binding screw. A soft iron cylinder is placed symmetrically inside the coil. The hemispherical magnetic poles produce a radial magnetic field in which the plane of the coil is parallel to the magnetic field in all its positions. A small plane mirror attached to the suspension wire is used along with a lamp and scale arrangement to measure the deflection of the coil.

### Working of Moving Coil Galvanometer

Let PQRS be a single turn of the coil. A current I flows through the coil. In a radial magnetic field, the plane of the coil is always parallel to the magnetic field. Hence the sides QR and SP are always parallel to the field. So, they do not experience any force. The sides PQ and RS are always perpendicular to the field.

PQ = RS = l, length of the coil and PS = QR = b, breadth of the coil. Force on PQ, F = BI (PQ) = BIl. According to Flemingâ€™s left-hand rule, this force is normal to the plane of the coil and acts outwards.

Force on RS, F = BI (RS) = BIl. This force is normal to the plane of the coil and acts inwards. These two equal, oppositely directed parallel forces having different lines of action constitute a couple and deflect the coil. If there are n turns in the coil, the moment of the deflecting couple = n BIl – b

Hence the moment of the deflecting couple = nBIA

The suspension wire twists when the coil deflects. On account of elasticity, a restoring couple is set up in the wire. This couple is proportional to the twist. If Î¸ is the angular twist, then, the moment of the restoring couple = CÎ¸, where C is the restoring couple per unit twist. At equilibrium, deflecting couple = restoring couple nBIA = CÎ¸

Hence we can write, nBIA = CÎ¸

I = (C / nBA) Ã— Î¸ where C is the torsional constant of the spring; i.e. the restoring torque per unit twist. A pointer attached to the spring indicates the deflection Î¸ on the scale.

Learn about Magnetic Force and Magnetic Field here

## The Sensitivity of Moving Coil Galvanometer

The sensitivity of a Moving Coil Galvanometer is the ratio of the change in deflection of the galvanometer to the change in current. Therefore we write, Sensitivity = dÎ¸/di. If a galvanometer gives a larger deflection for a small current it is a sensitive galvanometer. The current in Moving Coil galvanometer is: I = (C/nBA) Ã— Î¸

Therefore, Î¸ = (nBA/C) Ã— I. Differentiating on both sides wrt I, we have: dÎ¸/di = (nBA/C).

To sum up, the sensitivity of Moving Coil Galvanometer increases by:

• Increasing the no. of turns and the area of the coil,
• Increasing the magnetic induction and
• Decreasing the couple per unit twist of the suspension fibre.

• Sensitivity increases as the value of n, B, A increases and value of k decreases.
• The eddy currents produced in the frame bring the coil to rest quickly, due to the coil wound over the metallic frame.

• We cannot change the sensitivity of the galvanometer at will.

## Solved Examples for You

Question: Assertion: The resistance of a milliammeter is greater than that of the ammeter

Reason: Shunt resistance in case of a milliammeter is more than that of the ammeter.

1. Both (A) and (R) are true and (R) is the correct explanation of (A).
2. Both (A) and (R) are true but (R) is not the correct explanation of (A).
3. (A) is true but (R) is false.
4. (A) is false but (R) is true.

Solution: Unlike voltmeter, to have a more accurate reading in the ammeter, the whole current should pass through the ammeter for which the shunt resistance should be much high. Therefore the resistance of milliammeter is more than just ammeter.

Question: Moving Coil Galvanometer uses phosphor-bronze wire for suspension because it has

1. High Conductivity
2. High Sensitivity
3. A large couple per unit twist
4. A small couple per unit twist

Solution: We know that the restoring torque is Ï„ = CÎ¸. As K is torsional constant. However the value of C is very small in phosphor-bronze wire, a small restoring torque is generated in the wire. That is, in other words, the Phosphor-bronze wire has a small couple per unit twist.

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### One response to “Magnetic Field Due to a Current Element, Biot-Savart Law”

1. Wasique Azmi says:

What about 2 m magnetic feild? They hv not asked at centre!!!!!