Moving Coil Galvanometer - "Dead-Beat Galvanometer" (Pivoted Type) and its conversion to ammeter and voltmeter

Principle

 It is based on the principle that whenever a loop carrying current is placed in a magnetic field, it experiences a torque which tends to rotate it. 

Construction

It consists of a coil 'C' having a large number of turns of thin copper wire. The coil is suspended from a torsion head T by means of a fine suspension fibre of phosphor bronze in such a way that it hangs in between the cylindrical pole pieces N and S of a horse shoe magnet. A soft iron cylindrical core 'K' is adjusted inside the coil in such a way that the coil touches neither the pole pieces nor the core. One end of the coil is soldered to a suspension fibre F through a small plane mirror M while the other end is connected to a delicate spring S of phosphor bronze. The torsion head and the spring are internally connected to the terminals A and B to pass current through the galvanometer [Fig. 1(i)].

Theory

When a closed loop is suspended in a magnetic field, it experiences a torque τ which tends to rotate it about a vertical axis, 

           τ = nBiA cos θ

     Here, n is the number of turns of the coil of area A, i is the current passing through it. B is the strength of magnetic field due to magnet NS and θ is the angle which the plane of the coil makes with the magnetic field. 

Fig. 1. Moving coil galvanometer. 

     Since the pole pieces are of cylindrical form, the lines of force will be along the radius. Therefore as the coil rotates, its plane will always be parallel to the  direction of lines of force, in all its positions, as shown in Fig. 1(ii). Such a field is known as radial field. 

      For a radial field,       

                 θ = 0

∴               τ = nBiA                (∵  cos θ = 1) 

     As a result of this couple, the coil gets deflected. This produces a twist in the suspension fibre, due to which the coil is acted upon by the another couple called restoring couple which tends to take it back to the original position. 

     If C is the torsional couple per unit angular twist of the fibre, then

     Moment of the restoring couple = Cθ

     In equilibrium position, the torque due to deflecting couple must balance that due to the restoring couple. 

i.e.,             nBiA = Cθ

or                      i = C/nBA . θ

or                      i = Kθ

where  K = C/nBA is known as the reduction factor of the moving coil galvanometer and is constant for a galvanometer. 

     Hence, the current passing through the galvanometer is directly proportional to the direction. 

     If  θ = 1,   then   i = K. 

     Thus, the reduction factor of moving coil galvanometer is defined as the current required to produce a unit deflection in the galvanometer. 

Working

The levelling screws are adjusted for levelling the instrument. The torsion head is set so that the coil hangs freely without touching the poles or the soft iron core. The current to be measured is now passed through the terminals A and B. It will be observed that the coil gets deflected. The deflection can be measured by using a lamp and scale arrangement which consists of  lamp L mounted on a vertical stand. A fine collimated beam from the lamp is focussed on to the mirror M. The reflected beam is received on a semi-transparent scale 'S' mounted on the same stand [Fig. 2]. As the mirror gets deflected, a bright circular spot moves over the scale graduated in centimetres. Thus, the deflection of the coil can be measured. 

Fig. 2. Lamp and scale arrangement. 

Merits

A moving coil galvanometer has following merits :

1. It is a highly sensitive instrument and hence can be used to measure very small currents.                                              
2. Since the electric current is proportional to the deflection produced, a linear scale can be used for measurement purposes.                             
3. Its magnet produces a strong magnetic field within the neighborhood of coil. Therefore, the performance of the galvanometer cannot be affected by the presence of any stray magnet or magnetic substance nearby.                       
4. Like a tangent galvanometer, it does not require any specific setting. This is again due to its own strong magnetic field. 

  Demerits

1. It is not direct reading. We have to make a lot of adjustments to use this galvanometer.                                               
2. It is not portable.                                          
3. Its suspension fibre is very delicate. If due precaution is not taken, it gets broken too often. That is why the coil has to be locked while displacing the galvanometer from one place to the other.                                                               
4. A lot of space (for setting up a lamp and a scale arrangement) is required for its operation. 

SENSITIVITY OF A GALVANOMETER

The sensitivity of an instrument is measured by the minimum input required for a certain standard output. In case of a galvanometer employing the use of a lamp and a scale arrangement, the standard output is a deflection of a spot of light by 1 mm on a scale clamped at a distance of 1 metre from the reflecting mirror of galvanometer. It is generally named as a u it deflection in the case. 

     (i) Current sensitivity. Current sensitivity of a galvanometer is defined as the minimum current required to produce a deflection of a spot of light by 1 mm on a scale fixed at a distance of 1 metre from the reflecting mirror of the galvanometer. 

     If 'θ' is the deflection produced in the coil due to a current i flowing through it, current sensitivity Si is given by

                 Si = i/θ = i/d

where 'd' is deflection in mm, of the spot on a screen placed 1 m away. 

    (ii) Voltage sensitivity. Voltage sensitivity of a galvanometer is defined as the minimum voltage which when applied across the galvanometer produced a deflection of a spot of light by 1 mm on a scale fixed at a distance of 1 metre from the reflecting mirror of the galvanometer. 

     If 'V' is the potential difference applied across the galvanometer of resistance G, current i flowing through it is

                 i = V/G

     For moving coil galvanometer, 

                  i = C/nHA . θ        

∴          V/G = C/nHA . θ 

     Voltage sensitivity of the galvanometer

                Sv = V/θ = iG/d = CG/nAH

     It should be clearly noted that smaller the value of 'Si' or 'Sv', more sensitive is the galvanometer. Thus, to make a galvanometer more sensitive we should aim at having values if 'Si' and 'Sv' as small as possible. This can be achieved in a number of ways. 

     (i) By increasing n. An increase in the number of turns of galvanometer will make it more sensitive. But we can't increase n indefinitely to a very large value. This will the resistance 'G' of a galvanometer which will result in increase of Sv . 

    (ii) By increasing A. An increase in area of coil results in decrease of Si or Sv thereby making the galvanometer more sensitive. The magnetic field of the radial field is uniform over a narrow region. If the area of the coil is extraordinary large, some portion of the coil will be out of the region of uniform field. So we can't increase the area indefinitely. 

   (iii) By increasing B. To have a large B we must have a bigger magnet. This results in an abnormal increase in size of galvanometer. 

    (iv) By decreasing C. A galvanometer can be made highly sensitive by making use of a suspension fibre which has a small value of C. For a suspension fibre

                       C =  π η r⁴/2l

where l = length of fibre, r = radius of fibre and η = modulus of rigidity of the material of fibre. 

     'C' can be decreased by making use of a long (longer l), thin (smaller r) and silken (lesser η) fibre. Since C ∝ r⁴, a decrease in radius of fibre will be much more effective in increasing sensitivity of galvanometer. 

Experimental determination

     The circuit diagram for experimental determination of current and voltage sensitives of a galvanometer is shown in Fig. 3.

Fig. 3. Determination of sensitivity of galvanometer. 

     A source of e.m.f., E is connected to resistance 'S' and 'r' in series through a key. A galvanometer having high resistance R in series, is connected across BC. This ensures that effective resistance in between B and C is r. [∵  r << R + G]

     Let V and v be the potential difference (to be measured with a voltmeter) across AC and BC. 

           v/V = r/S + r        or        v = Vr/S + r 

     If i is the current flowing in the galvanometer, 

            i = v/R + G = Vr/(S + r) (R + G) 

     Current sensitivity, 

          Sv = iG/d = Vr/d(S + r) (R + G) × G

     Here 'd' is deflection of spot of light, in mm, on a screen placed at a distance of 1 metre from the mirror of galvanometer. 

WESTON TYPE GALVANOMETER

In order to avoid the difficult adjustment of D'Arsonval type moving coil galvanometer, Dr. Weston modified it to make it a direct reading instrument without making use of lamp and scale arrangement. This modified type is called pointer type galvanometer. The coil having a few number of turns of copper wire, wound on a metal frame, is mounted on a spindle. The ends of the spindle are fixed in two jewelled bearings to reduce friction. The coil is placed in between the two pole pieces of a horse shoe magnet having cylindrical pole pieces which provide a strong radial field. The restoring couple controls the rotation of the coil. This couple is provided by two very delicate springs attached with the spindle. 

     A light aluminium pointer is attached to the spindle. The whole apparatus is enclosed in a bakelite cover. As the coil rotates, the pointer slides over a scale as shown in Fig. 4.

Fig. 4. Weston type galvanometer. 

     A source of current is connected between the terminals, A and B. When the current passes through the coil, it experiences a deflecting couple which deflects it. When the deflecting couple due to the current balances the restoring couple provided by the springs, the coil comes to rest. The deflection can be measured by noting the reading of pointer on the scale. 

CONVERSION OF AN GALVANOMETER INTO AN AMMETER

An ammeter is the instrument used for measurement of current in a circuit. 

     Galvanometers are generally very sensitive. Current of small value takes the pointer out of scale. It may even damage the coil. Thus, it is dangerous to expose a galvanometer directly to an unknown current without doing any arrangement for its safety. 

     A galvanometer is rendered safe when a suitable low resistance 'S' is connected across the terminals A and B and is in parallel with the galvanometer coil. The resistance 'S' provides a bypass for the excess current. 

     The value of 'S' to be connected in parallel with coil is selected in such a way that when the combination of S and G, in parallel, is exposed to current 'i' (to be measured), the galvanometer takes a current 'ig' only [Fig. 5(i)]. Here ig is the current required for full scale deflection in the galvanometer. 

     If ig is the current passing through the shunt, then

                i = ig + is

 ∴              is = i - ig

 

Fig. 5. Conversion of a galvanometer into an ammeter. 

  

      Since G and S are in parallel, 

∴          is / ig = G/S    or       S = Gig /ig  = Gig / i - ig

     Knowing the value of G, I and ig the values of S can be calculated. A Weston type galvanometer having a calculated low resistance S connected in parallel with it is called an ammeter [Fig. 5(ii)]. The pointer is fixed in such a way that in 'no current position', it stands at zero mark on the extreme left to the scale. 

     The terminals A and B are marked '+' and '-' respectively so as to send the current through the instrument in one direction only. 

     The presence of a resistance 'S', in parallel, results in the decrease of resistance of the galvanometer. Thus, an ammeter is an ammeter is a low resistance galvanometer and is, therefore, always connected in series with the circuit. 

CONVERSION OF A GALVANOMETER INTO A VOLTMETER

A voltmeter is an instrument used for measuring the potential difference between two points. 

     To convert a galvanometer into a voltmeter, a suitable high resistance R is connected in series with the galvanometer coil. The value of 'R' is so selected that when the combination is exposed to full potential difference V, the current passing through the voltmeter should be 'ig' [Fig. 6(i)]. Hence, ig is the current required for full scale deflection. 

or              R + G = V/ig

∴                       R = V/ig - G 

Fig. 6. Conversion of a galvanometer into a voltmeter. 

     Knowing the values of V, ig and G, th3 value of 'R' can be calculated. A Weston type galvanometer having a high resistance R in series with galvanometer coil is shown in Fig. 6(ii).

     The presence of a high resistance 'R' in series with the galvanometer coil results in the increase in resistance of the galvanometer. Thus, a voltmeter is a high resistance galvanometer and is, therefore, always connected in parallel with the circuit. 

IMPORTANT NOTES

1. Galvanometer is a current detecting device. That is why its pointer is in the centre of scale since we must be prepared for any direction of current. In case of ammeter and voltmeter the zero position of the pointer is on one side of scale since we know the direction of current. This helps in increasing the sensitivity of the instrument. 2. A low resistance connected in parallel with a circuit decreases its resistance drastically. Therefore, an ammeter, being a low resistance instrument, is always connected in series with the circuit.                                                   3. A high resistance connected in series with the circuit increases its resistance drastically. Therefore, a voltmeter, being a high resistance instrument, is always connected in parallel with the circuit.

Examples

Example 1. 

     The resistance of a galvanometer is 49 ohm and the maximum current which can be passed through it is 0.001 A. What resistance must be connected to it in order to convert it into : (i) an ammeter if range 0.5 A, (ii) a voltmeter of range 5 V ? 

 Solution. 

     Given, G = 49 ohm,  ig = 0.001 A

     (i) For ammeter,    i = 0.5 A. 

     Value of shunt 'S' is,

          S = Gig/i - ig = 49 × 0.001/(0.5 - 0.001) Ω

             = 49 × 0.001/0.499 Ω

             = 0.098 ohm. 

     So the galvanometer converted into an ammeter of range 0.5 A by connecting a resistance of 0.098 ohm in parallel with the coil of galvanometer. 

    (ii) For voltmeter, 

             R = V/ig - G,           V = 5 V, 

             ig = 0.001 A,          G = 490 ohm

            R = [5/0.001 - 49] Ω

               = (5000 - 49) Ω 

               = 4951 ohm. 

     Thus, the galvanometer can be converted into a voltmeter of range 5 V by connecting a resistance of 4951 ohm in series with the galvanometer coil. 

Example 2.

     A battery of e.m.f. 1.4 V and internal resistance 2 Ω is connected to a resistor of 100 Ω through an ammeter. The resistance of the ammeter is 4/3 Ω. A voltmeter has also been connected to find the potential difference across the resistor. Draw the circuit diagram. If the ammeter reads 0.02 A, what is the resistance of the voltmeter ? The voltmeter reads 1.10 V, what is the error in the reading ? 

Solution. 

     Let R = resistance of voltmeter

     If R' = resistance of parallel combination of 100 Ω and R, 

                  R' = 100 R/100 + R                  ....(i) 

Fig. 7.

     Total resistance of the circuit = 2 + 4/3 + 100 R/100 + R

               i = E.M.F./Total resistance

         0.02 = 1.4/2 + 4/3 + 100 R/100 + R

         0.02 = 1.4 (100 + R) ×3/6 (100 + R) + 4 (100 + R) + 300 R

     0.02 × 6 × (100 + R) + 0.02 × 4 × (100 + R) + 0.02 × 300 R = 1.4 × 100 × 3 + 1.4 × 3R

     12 + 0.12 R + 8 + 0.08 R + 6 R = 420 + 4.2 R

                                                  2 R = 400

                                                     R = 200

     ∴  Resistance of voltmeter = 200 ohm. 

     Substituting for R in equation (i)

               R' = 100 × 200/100 + 200 Ω

     ∴  Reading of voltmeter = i × R' 

                                                 = 0.02 × 200/3 V

                                                 = 4/3 V

                                                 = 1.33 V

     Error in the reading of voltmeter

                   = 1.33 V - 1.10 V

                   = 0.23 V. 

Example 3.

     A galvanometer, together with an unknown resistance in series is connected across two identical batteries each of 1.5 V. When the batteries are connected in series, the galvanometer records a current of 1 A and when the batteries are connected in parallel the current is 0.6 A. What is the internal resistance of the battery ? 

Solution. 

     Let R = unknown resistance in the circuit (including that of galvanometer) 

            r = internal resistance of each battery. 

     Case (i) When the batteries are connected in series [Fig. 8(i)]

     Total internal resistance = 2r

     Total resistance of the circuit = R + 2r

     Total e.m.f. of the circuit = 1.5 V + 1.5 V

                                                  = 3 V. 

     ∴                i₁ = 3/R +2r

    Since         i₁ = 1            ∴ = 3/R + 2r

    ∴        R + 2r = 3                                  ... (i) 

Fig. 8. 

     Case (ii) When the two batteries are connected in parallel [Fig. 8(ii)]

     Total internal resistance = r × r/r + r

                                                  = r²/2r = r/2

     Total resistance of the circuit = R + r/2

     Total e.m.f. of the circuit = 1.5 V

     ∴                i₂ = 1.5/R + r/2 = 1.5 × 2/2R + 2

     Since        i₂ = 0.6

     ∴             0.6 = 1.5 × 2/2R + r

     ∴       2R + r = 3                                   ... (ii) 

     Multiplying (i) by 2 and subtracting (ii) from it. 

              2R + 4r - 2R - r = 6 - 5 = 1

                                   3R = 1

     ∴                              r = 1/3 Ω.