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