## What is a Permanent Magnet Moving Coil (PMMC)?

A **Permanent Magnet Moving Coil** (**PMMC**) meter – also known as a **D’Arsonval meter** or **galvanometer** – is an instrument that allows you to measure the current through a coil by observing the coil’s angular deflection in a uniform magnetic field.

A PMMC meter places a coil of wire (i.e. a conductor) inbetween two permanent magnets in order to create stationary magnetic field. According to Faraday’s Laws of electromagnetic induction, a current carrying conductor placed in a magnetic field will experience a force in the direction determined by Fleming’s left hand rule.

The magnitude (strength) of this force will be proportional to the amount of current through the wire. A pointer is attached to the end of the wire and it is put along a scale.

When the torques are balanced the moving coil will stop, and its angular deflection can be measured by the scale. If the permanent magnet fiel is uniform and the spring linear, then the pointer deflection is also linear. Hence we can use this linear relationship to determine the amount of electrical current passing through the wire.

PMMC instruments (i.e. D’Arsonval meters) are only used for measuring the Direct Current (DC) current. If we were to use Alternating Current (AC) current, the direction of current will be reversed during the negative half cycle, and hence the direction of torque will also be reversed. This results in an average value of zero torque – hence no net movement against the scale.

Despite this, PMMC meters can accurately measure DC current.

If you’d prefer a video explanation, here is a video on **Permanent Magnet Moving Coils**:

## PMMC Construction

A PMMC meter (or D’Arsonval meters) is constructed of 5 main components:

- Stationary Part or Magnet System
- Moving Coil
- Control System
- Damping System
- Meter

### Stationary Part or Magnet System

In the present time we use magnets of high field intensities, high coercive force instead of using U shaped permanent magnet having soft iron pole pieces. The magnets which we are using nowadays are made up of materials like alcomax and alnico which provide high field strength.

### Moving Coil

The moving coil can freely moves between the two permanent magnets as shown in the figure given below. The coil is wound with many turns of copper wire and is placed on rectangular aluminium which is pivoted on jeweled bearings.

### Control System

The spring generally acts as control system for **PMMC instruments**. The spring also serves another important function by providing the path to lead current in and out of the coil.

### Damping System

The damping force hence torque is provided by movement of aluminium former in the magnetic field created by the permanent magnets.

### Meter

Meter of these instruments consists of light weight pointer to have free movement and scale which is linear or uniform and varies with angle.

## PMMC Torque Equation

Let us derive a general expression for torque in permanent magnet moving coil instruments or **PMMC instruments**. We know that in moving coil instruments the deflecting torque is given by the expression:

- T
_{d}= NBldI where N is number of turns, - B is magnetic flux density in air gap,
- l is the length of moving coil,
- d is the width of the moving coil,
- I is the electric current.

Now for a moving coil instrument the deflecting torque should be proportional to current, mathematically we can write T_{d} = GI. Thus on comparing we say G = NBIdl. At steady state we have both the controlling and deflecting torques are equal. T_{c} is controlling torque, on equating controlling torque with deflection torque we have

GI = K.x where x is deflection thus current is given by

Since the deflection is directly proportional to the current therefore we need a uniform scale on the meter for measurement of current.

Now we are going to discuss about the basic circuit diagram of the ammeter. Let us consider a circuit as shown below:

The current I is shown which breaks into two components at the point A. The two components are I_{s} and I_{m}. Before I comment on the magnitude values of these currents, let us know more about the construction of shunt resistance. The basic properties of shunt resistance are written below,

The electrical resistance of these shunts should not differ at higher temperature, it they should posses very low value of temperature coefficient. Also the resistance should be time independent. Last and the most important property they should posses is that they should be able to carry high value of current without much rise in temperature. Usually manganin is used for making DC resistance. Thus we can say that the value of I_{s} much greater than the value of I_{m} as resistance of shunt is low. From the we have,

Where, R_{s} is resistance of shunt and R_{m} is the electrical resistance of the coil.

From the above two equations we can write,

Where, m is the magnifying power of the shunt.

### Errors in Permanent Magnet Moving Coil Instruments

There are three main types of errors:

**Errors due to permanent magnets:**Due to temperature effects and aging of the magnets the magnet may lose their magnetism to some extent. The magnets are generally aged by the heat and vibration treatment.- Error may appear in PMMC Instrument due to the aging of the spring. However the error caused by the aging of the spring and the errors caused due to permanent magnet are opposite to each other, hence both the errors are compensated with each other.
**Change in the resistance of the moving coil with the temperature:**Generally the temperature coefficients of the value of coefficient of copper wire in moving coil is 0.04 per degree celsius rise in temperature. Due to lower value of temperature coefficient the temperature rises at faster rate and hence the resistance increases. Due to this significant amount of error is caused.

### Advantages of Permanent Magnet Moving Coil Instruments

The advantages of PMMC instruments are:

- The scale is uniformly divided as the current is directly proportional to deflection of the pointer. Hence it is very easy to measure quantities from these instruments.
- Power consumption is also very low in these types of instruments.
- A high torque to weight ratio.
- These are having multiple advantages, a single instrument can be used for measuring various quantities by using different values of shunts and multipliers.

### Disadvantages of Permanent Magnet Moving Coil Instruments

The disadvantages of PMMC instruments are:

- These instruments cannot measure AC quantities.
- The cost of these instruments is high as compared to moving iron instruments.