**Introduction**

The **PMMC** is **P**ermanent **M**oving **M**agnetic **C**oil is instrument contain copper wire winded around permanent magnet. The PMMC is a low level dc ammeter used in labs to perform experiments.

**PMMC instrument**

There are 3 forces involved in PMMC

1) Deflecting Force

2) Controlling Force

3) Damping force

Before discussing forces applied in PMMC first we need to know its parts.

1) Pointer

2) Two U-shaped permanent magnets

3) Core

4) Coil

5) Spiral Spring

**Working Principle**

It works on principle of Fleming’s Left Hand Rule. Thumb showing its **motion** first finger representing its **current** direction and second finger represents its **field**.

Now, back to forces these forces applied when current is flowing or not flowing.

1) **Deflecting Force**

When current passes through the coils it creates deflecting force which cause the pointer to move from its initial position. The distance between magnetic poles and light-weighted coils should be very less so maximum field can pass through it. Coils did not fixed but the pointer fixed to the coil it moves over the scale as coil rotates. Remember when current passes the deflecting force is magnetic.

2) **Controlling Force**

When no current passes through the coil pointer is at zero position the main element for controlling force is spiral spring but when current passes the pointer wind up as coil rotates. The coil and pointer stop rotating when deflecting and controlling force become equal to each other or magnetic and electric force become equal to each other.

3) **Damping Force**

The turning effect of force is called torque. Example when we open a door we applying force on it and it starts moving in specific axis. So when in PMMC electric and magnetic forces become equal to each other we can see damping (to and fro) effect on pointer damping force is required to minimize that oscillations. The damping force is normally provided by eddy currents.

**Inside view of PMMC**

Between pivot and jewel bearing we use springs which are not more reliable if by chance we drop the meter then it will not provide us accurate reading. Instead of this we can use taut-band method. In this method we use different clips instead of springs.

This is how it actually looks like

In damping force we discussed about Torque but why we used torque in PMMC because when current passes through coil the force exerted on each side of the coil and we know that

F=BIL newtons

Where B is the magnetic flux density I is current and L is length of coil in meters. As stated force applied on each side so multiply equation with 2 and there are N number of turns in it so equation take form

F=2BILN

But the force acting on it produce deflecting torque so it takes form

T=BLIND

Where D is diameter of the coil.

**Example:** A PMMC instrument with a 100 turns coil has a magnetic flux density it its air gaps of B=0.2T. The coil dimensions are D=1cm and l=1.5cm. Calculate the torque on the coil for the current of 1mA.

**Solution:** T_{D}= BLIND

= 0.2T * 1.5*10^{-2} * 1mA * 100 * 1*10^{-2}

= 3*10^{-6} N.m

**galvanometer**

is a device used to detect current. With appropriate modification we can convert it into dc ammeter to measure current in very large amount or in very small amount or dc voltmeter to measure dc voltage.

**Construction:**

A light rectangular frame on which a coil of thin copper wire is wound is pivoted between two almost frictionless pivots and placed between cylindrical poles of a permanent magnet that it can freely rotate in the region between two poles when current passes through these coils torque produces in it. Galvanometer are usually used to detect current or voltage in a circuit but not to measure there actual level.

**Ammeter**

If we connect a resistance with galvanometer and shunt resistance R_{sh }in parallel with galvanometer. Ammeter is always connected in series to avoid affecting the current level in circuit the ammeter must have resistance much lower than the circuit resistance.

**voltmeter**

Galvanometer can be converted into voltmeter by connecting a resistance in series with galvanometer. The value of resistance depends upon the range of voltmeter. In series connection the current through the galvanometer is same as that due to the resistance.

R_{t }= R + R_{g}

i_{g }= V / R + R_{g}

The meter that we discussed above is used to measure dc voltage.

**rectifier voltmeter**

We discussed above about dc meters and there working but now we learn about ac meters so there main task is rectification. Rectification is basically used to convert ac current to dc current there are two types of rectification 1- Full-wave rectification 2- Half-wave rectification. So the same concept applied on ac voltmeters and ammeters.

**full-wave rectifier voltmeter**

In rectification the most important component is diode (silicon or germanium) and we use wheat-stone bridge for FWR. The whole topic is discussed in http://www.electricalengineering4u.com/electronic-devices-and-circuit/applications-of-diode/

The meter deflection is proportional to average current I_{avg} and we know that I_{avg}=I_{m}×0.637 . The current which we obtain is rms to convert it into peak value we just multiply it by 0.707.

Note: These meters can only convert sine wave voltages into peak not any wave other than sine wave is detected.

**half-wave rectifier voltmeter**

How half-wave rectifier works is discussed in http://www.electricalengineering4u.com/electronic-devices-and-circuit/applications-of-diode

The waveform of the voltage across meter and Rsh is a series of positive half-cycles with intervening spaces. In HWR I_{av}=0.5(0.637I_{m})

**series ohmmeter**

We already know that Ohm is unit of resistance so ohmmeter is use to measure resistance.Now a days they are present in DMM but there is not such a separate instrument. How they form? A series circuit which contain a voltage source,a standard resistor, low current PMMC and a measurable resistor connected with two terminals.

Lets talk about parameters present in this fig and how to calculate them. E is battery R_{m} is meter resistance

R_{1} is standard resistance and R_{x} is Measurable resistance I_{m} is meter current by applying Ohm’s law we can calculate it as

I_{m }= E / R_{x }+ R_{m }+ R_{1}

If we short-circuited the points A and B or remove resistance R_{x }Then we obtain equation

I_{m }= E / R_{m }+ R_{1}

but if the value of Rx ranges between zero or infinity than the meter current is greater than zero but not greater than FSD.

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