Hello and welcome. So, this is our first class in Electrical Measurement and Instrumentation.

In this video, we shall learn about how an ammeter works.

So, the topic is working principle of an ammeter. So, we will talk about a particular type of

ammeter, which we also sometimes call a permanent magnet moving coil instrument

and in short we call it PMMC. So, we shall see how does this emitter works? So, as you

know emitters measure current. So, we will have an instrument which can measure current.

So, let us look at the constructional detail of this instrument. It is composed of mainly

a permanent magnet a U-shaped permanent magnet which has 2 poles.

So, the magnet looks like this, it has it is like a U. It is a U shaped magnet and it

has 2 poles; one of them north, another south. The pole face is curved like this. It is like

a inner surface of a cylinder ok. So, these are the 2 poles and this is a permanent magnet.

And then we have a cylindrical core inside this vacant cylindrical region. So, the core

which is made up of some soft iron soft magnetic material, which is like a cylinder is placed

here inside this 2 poles. So, this is a cylinder inside the 2 poles. Now, we have a coil and

the coil is owned on top of a rectangular frame. So, let me first draw a rectangular

frame. So, this is a rectangular frame often made

up of aluminium and then we have copper coil owned on top of it. So, the coil starts like

this. So, this is one end of the coil and then the conductor goes like this, round this

frame, then like this and then it comes back. So, this is one complete turn and then it

can go again, round and round. So, round and round this aluminium frame and then the other

terminal comes out like this. So, this is one terminal of the coil, this is another

terminal of the coil and this is owned on top of an aluminium rectangular frame.

So, this is copper (Cu) for copper and this frame is made up of aluminium (Al) normally.

And then we put this coil, this form mode of frame on top of this cylindrical structure.

So, we put this like this may be. So, the coil is put around this core, a soft iron

core. So, this is a soft iron core and this is the coil and the coil is actually like

this. So, it can have many turns and then finally, the other end comes out from the

bottom of this form. So, let me draw this coil here once again

and the other end is here. So now, what will happen if we pass some current through this

coil? You know that these current carrying conductors or these coils, they are in a magnetic

field. And therefore, they will experience some force and therefore, some torque and

then the coil will try to rotate, that is the basic principle of this instrument. Now

to see it in more detail, let me take a cross section of this instrument may be like, this

let me take a cross section. So, let me cut this instrument along this dashed line and

see it from the front. So, how will it look like? So, it will look

like these 2 poles, like 2 rectangles; north and south and between these 2 poles, we have

this coil. So, we have this coil which is like this. So, this is one turn, this is another

turn, it can have many turns, 100’s of turns and then it then the other end comes out from

the bottom. And inside this coil we have the core. This cylindrical core which will look

like a rectangle as seen from the front view. Note that the core and the coil, they are

not touching each other, they are separate; they are not attached to each other. So, the

coil can move independently from this core. So, the core does not move, but the coil can

move. So, this is how it looks like from the front view. Now, suppose there is a current

which is flowing like this, which means it is going like, this from top to bottom on

the left side and from bottom to top on the right side.

Now, what will happen? We will have magnetic lines of forces, passing from left to right;

that means, from north to south like this. And these current carrying conductors, they

are inside this magnetic field. So, they will experience some electromagnetic force. And

the direction of the electromagnetic force can be found using the left hand rule of Fleming’s.

So, let us apply Fleming’s left hand rule. Now let me now apply Flemings left hand rule.

So, I have 3 fingers and the first finger should point towards the flux lines, which

is from left to right according to my drawing. And then this middle finger should be along

the direction of the current. If I am considering this left side of the coil, then this is the

direction of current. And then my thumb points upwards. So, that

means, the force acting on this side of the coil will be upwards, perpendicular to the

plane of paper and it is towards us i.e., upwards. So, the force will here will be upwards

ok. So, let me also draw the top view for ease of visualization. So, this is front view.

Let me draw the top view of this. So, the top view will look like 2 poles north,

south and at the center we have this cylindrical core, which looks like a circle from the top

and then we have this coils which is here. These are the turns and it looks like just

a line from the top ok. And as you have seen on this side the force is in this direction,

this is the direction of the force. Similarly, if we find the direction of force

on this side of the coil. So, let me use my hand once again. So, here the flux lines are

once again from left to right. The current is from bottom to up. So, like this and then

my thumb points downwards, perpendicular to the plane of paper, but inwards or away from

me. So, here the force will be like this. Now, this two forces together form a couple

or they apply a torque which tries to turn the coil in this anti-clockwise direction.

So, what we have seen, we have seen that if there is a current flowing through this conductor,

then we will have two forces acting on two sides of this coil which will try to turn

this coil. Now, the coil can get turned by indefinite

amount. So, the coil will turn indefinitely until it touches something or hit something,

because there is nothing to stop the coil from turning. So, therefore, what will happen?

No matter I mean whether the current is small or large, the coil will turn to it is maximum

possible angle. So, if so, even very small current can turn the coil to its maximum possible

angle. So, essentially

we cannot distinguish between small and large current or in other words we cannot measure

the amount of current, in this configuration. Now to be able to measure the amount of current,

we need another component in this construction which is a spring. So, we will take a spring

and we will connect it here. This is a spiral spring and the other end of this spring is

connected to the frame of the instrument. So, this end cannot move and this end is connected

to the coil. Similarly, we will have another spring here,

one end is connected to the body or the frame of the instrument and the other end to the

coil. So, now, what happens, as soon as the coil tries to move, the spring will oppose

the motion.

Now, the spring will oppose the rotation or motion of the coil. So, if the coil is turned

by an angle of theta, say this coil is turned by an angle of theta and has come here say

it’s here. So, this is the new position of the coil and this angle, call this angle

as theta. So, if the coil is turned by an angle of theta then these springs are twisted

and according to Hooke’s law, it will give an opposing torque. So, with the opposing

torque according to Hooke’s law is given by theta, the amount of twist or turn multiplied

by some constant k. So, this is spring constant. And then the coil will settle down at some

position where the opposing torque is equal as the turning torque. So, this is the mechanism.

Now, let us try to find out the expression for the turning torque. The torque due to

this current which tries to turn this coil. Now, this is also called the deflecting torque,

because it tries to deflect or turn the coil and we generally denote this as TD; D for

deflecting torque. Now, let us find the expression.

So, see that this flux density is B and say the length of this coil inside the magnetic

field, Call this length as L. And then this current, call this current as I which is flowing

through this coil and say this coil has N number of turns. So, let N be the number of

turns in this coil. Now, consider, say only one conductor.

So, the force on any one conductor on this side. So, consider just one conductor, one

particular conductor. So, this force is given by we know F is equal to BIL. So, this is

from our knowledge of physics, high school physics, we know that this force is given

by BIL, B is the flux density, I is the current through the conductor and L is the length

of this coil. Now, there are N turns. So, the total force

on N conductors, that will be F multiplied by N, which means BIL multiplied by N. So,

this will be this total force here. So, this force is BILN. Similarly, this force will

also be BILN, but this is acting in the opposite direction. Now, what will be the torque, the

torque will be given by this forces multiplied by the distance between the lines of actions

of these forces and that distance, So, this is the distance which is same as this distance.

So, this is basically the width of the coil. We also call it the diameter of the coil and

we can call it as D, but note that this is actually not the diameter of the coil. So,

this is not I mean because the coil is not circular at all. So, strictly speaking this

is not the diameter of the coil, but you can say this is the diameter of the core approximately,

but we generally call it the diameter of the coil often and let us call this distance as

D. So, D is this distance, between the 2 forces.

So, the torque will be the force BILN multiplied by the distance D. And then this will be equal

to you can write it as B L and D L and D, then N and then I.

Now, L the length and D is the diameter or width of the coil. So, L times D is the area

of this coil. So, this area this is A. So, we can write it as BAN I. So, this is the

expression for the deflecting torque. So, let me write this expression as TD equals

BAN multiplied by I. So, it is observed that TD is proportional to the current flowing

through the coil. So, more the current is the higher will be the torque which is trying

to deflect or turn this coil. So, this is the turning torque or deflecting

torque. Now, as we have already seen that there are springs which tries to oppose the

movement of this coil and it gives some opposing torque, which we can write as

opposing torque, that is spring torque, we also call it the controlling torque.

So, these are all the names of the same thing, this is given by Hooke’s law, K the spring

constant multiplied by theta, where theta is the angle of deflection or angle of turning.

Now, if I have a fixed amount of current. So, if I is constant then TD is constant and

this TD tries to rotate the coil. So, we will call this T C, the spring torque we will call

this as TC, C for controlling and, TC which is given as K theta. So, TD is trying to rotate

the coil. Therefore, theta will increase

and so, TC which is nothing but Ktheta, will also increase and at some point, both will

be equal. Why? Because the turning torque is constant

and this coil is turning and as it is turning theta this angle theta is increasing. So,

K theta is increasing and therefore, at some point K theta will be equal to TD. So, then

TC, which is same as Ktheta will become TD. So, this is what we call the equilibrium.

And then the coil can settle down at this particular position or this particular value

of theta, because then TC will be equal to TD. So, the 2 opposing torques are equal in

magnitude, but opposite in direction. So, then there will be no resultant torque and

the coil need not move further. So, this condition is called the equilibrium.

So, therefore at equilibrium TC and TD are equal; that means, the controlling torque

and the deflecting torque, which are opposite in direction, they will be equal in magnitude

and then we can write this TC as Ktheta and TD is this BAN multiplied by I. So, at equilibrium

theta will be equal to BANI divided by K. Now, see that all this terms BAN and K they

are all constants. Because, the area of the coil is constant, number of turns is a constant.

Once the instrument is manufactured, they are not going to change, flux density not

going to change, spring constant is not going to change. So, this is a constant and we can

write this as one common constant S say multiplied by I.

So, observe that theta, which is the final position of the coil, is given as S times

I, or we can say that this is proportional to I. So, more the current is, the position

or the angle theta of the coil will be higher. So, for example, if current is say 1 ampere,

then if theta is equal to say 5 degrees, then it for I equals say 3 amperes, theta will

be 5 degree multiplied by 3 or 15 degree. So, this is the working principle of this

instrument, which we call a PMMC instrument or Permanent Magnet Moving Coil Instrument

in short PMMC. This is also called D Arsonval’s Galvanometer. So, this is how we can measure

current, because when there is a current flowing through this through the coil, it will get

deflected by an angle theta, we can observe the value of theta and if we know the value

of S, this constant which is given by BAN by K, then we can immediately find the value

of the current. So, we observed the angle theta and therefore,

we can measure the current. So, this is the working principle of this instrument. Let

us meet in our next lecture. Thank you.