Explain the principle ,working and construction of moving coil galvanometer.

Principle:

Its working is based on the fact that when a current carrying coil is placed in a magnetic field, it experiences a torque.

Working:

Suppose the coil PQRS is suspended freely in the magnetic field.

Let

l = Length PQ or RS of the coil

b = Breadth QR or SP of the coil

n = Number of turns in the coil

Area of each turn of the coil, A = l × b

Let B = Strength of the magnetic field in which coil is suspended

I = Current passing through the coil in the direction PQRS

Let, at any instant, α be the angle which the normal drawn on the plane of the coil makes with the direction of magnetic field.

The rectangular coil carrying current when placed in the magnetic field experiences a torque whose magnitude is given by,

τ = nIBA sinα

Due to deflecting torque, the coil rotates and suspension wire gets twisted. A restoring torque is set up in the suspension wire.

Let θbe the twist produced in the phosphor bronze strip due to rotation of the coil and K be the restoring torque per unit twist of the phosphor bronze strip. Then,

Total restoring torque produced = kθ

In equilibrium position of the coil,

Deflecting torque = Restoring torque

∴ NIBA = kθ

Or,

Where, [constant for a galvanometer]

It is known as galvanometer constant.

Current sensitivity of the galvanometer is the deflection per unit current.
Voltage sensitivity is the deflection per unit voltage.

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Galvanometer is device used to detect current in a circuit.

Principle: A current carrying coil placed in a magnetic field experiences a current dependent torque which tends to rotate the coil, and thus produces an angular deflection.

Construction: A Weston (pivoted-type)(used in laboratories) galvanometer consists of a rectangular coil of insulated copper wire wound on a light non magnetic metallic (Aluminium) frame. This frame has got an axle. Both the ends of this axle are pivoted by jeweled bearings. The motion of the coil is controlled by a pair of hair springs of phosphor- bronze on both the ends which provide the restoring torque for the coil. These springs also act as current leads. A light aluminium pointer is also attached to the coil which helps to measure the deflection of the coil on the measuring scale. The coil is symmetrically placed between two cylindrical horse shoe magnets or, pole pieces of a strong permanent horse-shoe magnet. A cylindrical soft iron-core is also mounted. Since it has been mounted symmetrically between the concave cylindrical poles, the magnetic lines of force are allowed to act along the radius of the iron core. Thus, we get a radial magnetic field. The soft iron core due to its high permeability, intensifies the magnetic field. This increases the sensitivity of the galvanometer.

Theory and working:
Let:
I = current through the coil
a,b = Sides of the coil where, b is the side facing the magnets
A = ab = Area of the rectangular coil
N = Number of turns in the coil

As the magnetic field is radial, at every instant of time, the plane of the coil would be parallel to the magnetic field. The side a will also remain parallel to the magnetic field. Thus, the side a will not experience any force by the magnetic field. However, the side “b” of the coil would remain perpendicular to the magnetic field and thus experience a force. From Fleming’s left hand rule, we see that the two opposite “b” sides of the rectangular coil would experience equal and opposite force. This will constitute a couple and this will produce a torque.
This torque,
t = Force x perpendicular distance between the lines of action of the two forces
= BIbN x a sin(theta) where theta is the angle between the area vector and the magnetic field which is 90 degrees

So, the torque = BIbN x a = BINA

This torque deflects the coil by an angle alpha. A restoring torque acts on the coil, by the hair springs such that, restoring torque = k.alpha

where k is the torsion constant of the spring

Now, in equilibrium position,
k.alpha = BINA
Thus, alpha is directly proportional to I.
Thus, alpha = (NBA/k).I
Or, I = (k/NBA).alpha
Or, I = G.alpha

G is a constant, called Galvanometer constant and is constant for a galvanometer.

Meanwhile, the current which produces a deflection of one scale division is termed as the Figure of Merit of the galvanometer.

Sensitivity of a galvanometer: A galvanometer is said to be sensitive if it shows a large scale deflection even when a small amount of current is passed through it, or a small amount of voltage is applied across it.

CURRENT SENSITIVITY: The amount of deflection shown by a galvanometer when a unit current is passed through it. I(s) = alpha/I

VOLTAGE SENSITIVITY: The amount of deflection shown by a galvanometer when a unit potential difference is applied across the ends of the galvanometer. V(s) = alpha/V =alpha/IR = I(s)/R

[where, alpha = (NBA/k).I ]

Thus the factors on which the sensitivity of a moving coil galvanometer depends on, are:
1. Number of turns of the coil, N
2. Strength of magnetic field, B
3. Area of the rectangular coil, A
4. Torsion constant of the spring and the suspension wires, k

Cyclotron
Cyclotron is a device used to accelerate charged particles to high energies. It was devised by Lawrence.
Principle
Cyclotron works on the principle that a charged particle moving normal to a magnetic field experiences magnetic lorentz force due to which the particle moves in a circular path.
Construction

It consists of a hollow metal cylinder divided into two sections D1 and D2 called Dees, enclosed in an evacuated chamber (Fig 3.21). The Dees are kept separated and a source of ions is placed at the centre in the gap between the Dees. They are placed between the pole pieces of a strong electromagnet. The magnetic field acts perpendicular to the plane of the Dees. The Dees are connected to a high frequency oscillator.

Working:
When a positive ion of charge q and mass m is emitted from the source, it is accelerated towards the Dee having a negative potential at that instant of time. Due to the normal magnetic field, the ion experiences magnetic lorentz force and moves in a circular path. By the time the ion arrives at the gap between the Dees, the polarity of the Dees gets reversed. Hence the particle is once again accelerated and moves into the other Dee with a greater velocity along a circle of greater radius. Thus the particle moves in a spiral path of increasing radius and when it comes near the edge, it is taken out with the help of a deflector plate (D.P). The particle with high energy is now allowed to hit the target T.

When the particle moves along a circle of radius r with a velocity v, the magnetic Lorentz force provides the necessary centripetal force.

Bqv = (vm2 ) / r
v /r = Bq / m = constant ...(1)
The time taken to describe a semi-circle
t = π r / v               (2)
Substituting equation (1) in (2),
t = π m/ Bq                   .. (3)
It is clear from equation (3) that the time taken by the ion to describe a semi-circle is independent of
(i) the radius (r) of the path and (ii) the velocity (v) of the particle
Hence, period of rotation T = 2t
T = 2 π m / Bq = constant ...(4)
So, in a uniform magnetic field, the ion traverses all the circles in exactly the same time. The frequency of rotation of the particle,
v = 1 /T = Bq / 2 πm       .. (5)
If the high frequency oscillator is adjusted to produce oscillations of frequency as given in equation (5), resonance occurs.Cyclotron is used to accelerate protons, deutrons and α - particles.

Limitations
a.     Maintaining a uniform magnetic field over a large area of the Dees is difficult.
b.     At high velocities, relativistic variation of mass of the particle upsets the resonance condition.
c.      At high frequencies, relativistic variation of mass of the electron is appreciable and hence electrons cannot be accelerated by cyclotron.

Galvanometer

Definition: The galvanometer is the device used for detecting the presence of small current and voltage or for measuring their magnitude. The galvanometer is mainly used in the bridges and potentiometer where they indicate the null deflection or zero current.

Principle of Galvanometer

The potentiometer is based on the premise that the current sustaining coil is kept between the magnetic field experiences a torque.

Construction of the Galvanometer

The construction of the potentiometer is shown in the figure below.

The moving coil, suspension, and permanent magnet are the main parts of the galvanometer.

Moving Coil – The moving coil is the current carrying part of the galvanometer. It is rectangular or circular and has the number of turns of fine copper wire. The coil is freely moved about its vertical axis of symmetry between the poles of a permanent magnet. The iron core provides the low reluctance flux path and hence provides the strong magnetic field for the coil to move in.

Suspension – The coil is suspended by a flat ribbon which carries the current to the coil. The other current carrying coil is the lower suspension whose torque effect is negligible. The upper suspension coil is made up of gold or copper wire which is made in the form of a ribbon. The mechanical strength of the wire is not very strong, and hence the galvanometers handle carefully without any jerks.

Mirror – The suspension carries a small mirror which casts the beam of light. The beam of light placed on the scale on which the deflection is measured.

Torsion Head – The torsion head is used for controlling the position of the coil and for adjusting the zero setting.

Applications of Galvanometer

The galvanometer has following applications. They are

It is used for detecting the direction of current flows in the circuit. It also determines the null point of the circuit. The null point means the situation in which no current flows through the circuit.
It is used for measuring the current.
The voltage between any two points of the circuit is also determined through galvanometer.

Working of Galvanometer

Let, l, d – the length of respective vertical and horizontal side of the coil in the meter.
N – number of turns in the coil,
B – Flux density in the air gap, wb/m²
i – current through moving coil in Ampere
K – spring constant of suspension, Nm/rad
θ_f – final steady-state deflection of moving coil in radiance
When the current flows through the coil, it experiences a torque which is expressed as

The force on each side of the coil is given as,
Hence deflecting torque becomes, Where, N, B, A are the constant of the galvanometer.

The G is called the displacement constant of the galvanometer, and their value is equal NBA = NBld.

The controlling torque exerted by the suspension at deflection θ_F isFor final steady deflection, Hence final steady deflection,

For the small deflection angle, the deflection is expressed as the product of the radius and angle of the turned. By the reflected beam, it is expressed as 1000 Χ 2θ_F = 2000 Gi / K in millimetre.

The above equation shows that when the mirror turns through an angle θ_F the reflected beam turns through an angle 2θ_F shown in the figure below.

Conversion of Galvanometer into an Ammeter

The galvanometer is used as an ammeter by connecting the low resistance wire in parallel with the galvanometer. The potential difference between the voltage and the shunt resistance are equal.

Where, S = shunt resistance and I_s = current across the shunt.

As the galvanometer and the shunt resistance are connected in potential with the circuit, their potentials are equal.

Thus, the shunt resistance is given as,

The value of the shunt current is very small as compared to the supply current.

Conversion of Galvanometer into a voltmeter

The galvanometer is used as a voltmeter by connecting the high resistance in series with the circuit.

The range of the voltmeter depends on the value of the resistance connected in series with the circuit.

Principle
A current-carrying coil when placed in an external magnetic field experiences magnetic torque. The angle through which the coil is deflected due to the effect of the magnetic torque is proportional to the magnitude of current in the coil.

Working of Moving Coil Galvanometer

When a galvanometer is connected to a current carrying circuit, a current flows in the coil of the galvanometer.? Since the coil is suspended in a magnetic field, a?deflecting torque?acts upon it. Due to this torque, coil starts rotating from its position.
?
As the coil rotates, the controlling springs are twisted and an elastic restoring torque is developed in them and it opposes the rotation of the coil. This torque is proportional to the angle of rotation of the coil.
?
When the restoring torque (i.e.?controlling torque) becomes equal to the?deflecting torque, the coil rests in equilibrium position.
?
A galvanometer is used in electrical circuits to detect?current, and in experiments to determine the null point.
?
If somehow a heavy current happens to flow into the coil of the galvanometer, then due to very large deflection the pointer of the galvanometer may strike the ?stop pin? and be broken, or coil of the galvanometer may burn due to excessive heat produced.
?
To save the galvanometer from these possible damages, a thick wire or strip of copper is connected in parallel with its coil. It is known as ?shunt?.? Its resistance is very small as compared to the resistance of the coil. Therefore, most part of the current goes through the shunt and only a very small part goes through the coil. Hence, there are no chances of damage to the coil or pointer.
?
Shunted-galvanometer is very useful for determining the null-point in experiments. First, the approximate position of the null-point is determined by using the shunted-galvanometer. At this stage, the current in the circuit is very feeble. Now the shunt is removed from the galvanometer so that full current goes through the galvanometer and accurate position of the null-point is determined.

Moving-coil Galvanometer Construction
It consists of a coil having a large number of turns of fine insulated copper wire wound on an aluminum frame.
?
The ends of the axle of the aluminum frame are inserted in two pivots so that the coil may rotate about the axle. At both ends of the coil, near the pivots, two springs are attached which produce a controlling torque on the moving system and connect the coil to the outer circuit.
?On both sides of the coil, there are pole-pieces of a permanent strong horseshoe magnet. The coil rotates in the magnetic field of these pole pieces.
?
??To read the deflection of the coil, a pointer is attached to the coil which moves over a circular scale. The divisions on the scale are made at equal distances and the zero point is in the center. That is why no positive and negative signs are marked at the terminal screws of the galvanometer. It can measure currents up to 10-6?A.