EXPERIMENT : CONVERSION OF A GALVANOMETER INTO VOLTMETER

 AIM 

    To convert a given galvanometer into voltmeter of desired ranges and to calibrate it. 

APPARATUS USED 

    Galvanometer, voltmeter, connection wires, shunt resistance, key

WORKING PRINCIPLE 

    A galvanometer can be converted into voltmeter by connecting a high  resistance (shunt) wire series to it

Converting a galvanometer into a voltmeter

What is a voltmeter?

    Voltmeter is an instrument used to measure potential difference between the two ends of a current carrying conductor.

THEORY:

     A galvanometer can directly measure small potential differences only. To measure high potential differences, that is, to convert the galvanometer as voltmeter, some modifications has to be done in the galvanometer.

     Suppose to convert the galvanometer that can measure the potential difference up to V, the range of the voltmeter is 0 – V. For this, a suitable high resistance is connected in series with the galvanometer such that when a potential difference of V is applied, only a current Ig passes through the galvanometer as shown in the figure 1. 

Fig 1: Conversion of galvanometer into voltmeter

• A galvanometer can be converted in to a voltmeter by connecting a high resistance in series with it. 

• The scale is calibrated in volt. 

• The value of the resistance connected in series decides the range of the voltmeter.

FORMULA USED

To convert a galvanometer into a voltmeter of desired ranges, the resistance to be connected in series to it is given by.

  i) Shunt resistance, S = [V / I g  ] -G             --------> equation1

                      

                           Here,    

                                        S - shunt resistance in ohms 

                                        G - Resistance of galvanometer in Ohms. 

                                        I g - Current for full scale deflection in galvanometer in mA.

                                         v - Desired range of voltmeter in v. 

            ii) Ig is calculated using the equation,

  Ig = nk                         --------> equation2

                Where

                                 n - the number of divisions on the galvanometer (30 div)

                                 k - the figure of merit of galvanometer

            The figure of merit of a galvanometer is defined as the current required in producing a unit                     deflection in the scale of the galvanometer.  It is represented by the symbol k

                iii) K is given by the equation,

                                         K = E/ (P+Q) *P/d *1/G                --------> equation3

                        Where

                                        E - e.m.f. of the cell 

                                        G - deflection produced with resistance R

PROCEDURE

 Determination of Galvanometer Resistance (G) : 

Fig 2: Circuit diagram to find G

1. Take the circuit connection of figure in order to determine the resistance of the galvanometer by half deflection method. 

2. Introduce some high resistance Q (in the range 980 -999 ohm) and P (1-20 ohm)in the resistance box such that P +Q=1000 ohm.

3.If the deflection in the galvanometer goes out of scale bring it within the scale by adjusting the value of P,Q . 

4. Now, Increase the value of R ohm  in  resistance box. Adjust the value such that the deflection in galvanometer becomes half of its previous value.

OBSERVATION

From equation3,  

    the calculated value of figure of merit of a galvanometer(k)=2.1 x 10^-5 ampere/div

Substituing k in equation2,

   

    Current for full scale deflection in galvanometer(Ig) = 630 x 10^-6 ampere

From equation1, 

    To convert a galvanometer into a voltmeter of desired ranges(say, 10V),  the value of resistance(S) to be connected in series = 15,798 ohm

                                                               

Fig
3: Calibration galvanometer into a voltmeter

Full deflection in the galvanometer ie., 30 divisions is equal to 10V.

Then, 1V=3 divisions in galvanometer.

RESULT

    The given galvanometer is successfully converted into a voltmeter

EXPERIMENT : Determintion of moment of magnet by measuring field at points along the axis of a current carrying coil

   AIM

To study the field at a point along the axis of a current carrying circular coil   and  hence  to find moment of magnet

APPARATUS REQUIRED

Circular coil apparatus, compass box, rheostat, battery or power supply, ammeter, commutator, key and connecting wires.

FORMULA USED

 Field at a point along the axis of the coil is,

             nia² 

  F = ^___________      ampere/metre 

          2(a² + x²)^3/2

Where,

n -Number of turns in the coil 

i -current measued (A)

a -Radius of the coil (m)

x - distance between centre of coil and  centre of compass box (m)

Moment of magnet is,

                                                      𝜋nia2𝜇0(d2-l2)2

                                      M =   __________________        weber.metre

                                                         d(a2 + x2)3/2

Substituting F and 𝜇0 , we can reframe the equation as,

                                                  8𝜋2F(d2-l2)2

                                      M =   ____________ x 10-7       weber.metre

                                                         d

Where,

𝜇0 -Permittivity of free  space =4𝜋 x 10-7 Henry/metre

 l -semilength of magnet (m)

d- distance between centre of compass box and centre of bar magnet   (m)

CIRCUIT DIAGRAM

Figure 1: Circuit to find the field at points along
 the axis of the coil

PROCEDURE

The preliminary adjustments are carried out as follows

Figure 2: Circular coil apparatus with compass box 

• The leveling screws are adjusted so that the circular coil is vertical.

• The wooden bench is adjusted to be along the magnetic east-west direction

• A compass box is placed with its centre coinciding with the axis of the coil

• The compass box alone is rotated till the aluminium pointer reads 0° − 0°

                Electrical connections are made as shown in the circuit diagram (figure 1). The compass box is placed along its axis, with its centre at a distance x from the centre of the coil on one side. A suitable current (say, 1A) is passed through the coil by adjusting rheostat so that the deflection of the aluminium pointer lies between 30 º and 60 º. Two readings θ1 and θ2 corresponding to two ends of the pointer are noted. Now a bar magnet is placed along the axis of coil at a distance d1 from the centre of compass  box to make deflection 0-0 (as shown in figure 3).

Figure3: method to nulify the deflection using a magnet

    

        Now the direction of the current is reversed using commutator, two more readings θ3 and θ4 are

noted. The opposite pole of the magnet  at a distance d2 from the centre of compass  box  makes the

deflection 0-0. The experiment is repeated for another value of current,  keeping the compass box at the

same distance x.

OBSERVATION

Number of turns in the coil n= 30 turns

Circumference of the coil (2πa) = 45 cm

Radius of the coil a =0.073m

semilength of the magnet=0.038m

                                                                                                            Mean (M)= 1.7936 x10^-6  wm

Result:

i)The field at points along the axis of a current carrying circular coil is studied.

ii)The value of moment of magnet is  1.7936 x10^-6  wm