To Determine The Resistance of a Galvanometer by Half-Deflection Method.

Name of the Experiment: To Determine The Resistance of a Galvanometer by Half-Deflection Method.

Theory: In the arrangement shown in Fig. 01, if the shunt resistance (S) is very small compared to the galvanometer resistance R_G, then the potential difference (V) between the ends of the shunt resistance (S) remains nearly constant for all values of R₁.

Thus when R1=0, then the galvanometer current C_g is given by

            C_g =    = kd . . . . . . . . . . . . . . . (1)

Where d is the deflection of the spot of light on the scale and k is the galvanometer constant. If now a resistance R₁ is introduced in the galvanometer circuit such that the deflection reduces to   , then

C’_g =  = k  . . . . . .. . . . .. . . (2)

Where C’_g is the new galvanometer current.

Dividing (1) by (2), we get

=  =   

Or,  + R₁ = 2 

Or,  = R₁  . . . . .. . . . . . . . . . . . . (3)

Hence by simply measuring R1, R_G   can be found out.                          Fig. 1

Apparatus:

Zero point Galvanometer, Shunt Box S, Resistance R and R₁, Commutator K, Cell E, Connecting wires etc.

Procedure:  Make connection as shown in Fig. 1. Bring one sharp edge of the spot of light at the zero mark of the scale.

1. Insert a resistance (R) of the order of 1OOO ohms in the battery circuit. Make Rt = o by putting all the plugs in the box. Beginning with the smallest value (S = 0.1 ohm) of the shunt resistance S, go on increasing S until you obtain a deflection of about lO cm on the scale. Note this deflection.

2. keeping the resistance R constant, adjust the value of the resistance R1 until the deflection is reduced to half of the former. Record this value of R1 which is the value of the galvanometer resistance G.

3. Stop the current in the circuit and examine if the same sharp edge of the spot of light is still at zero of the scale. If not, adjust the scale to bring it to zero. Make the value of R1 zero and keep R the same. Now reverse the current with the commutator K. Repeat the whole operation to get another value of G

4.  Keeping the value of the resistance R the same, change the value of the shunt resistance S to obtain a different deflection of round about lO cm and similarly determine the value of G.

5.  Repeat the operation three times with different value of R in the battery circuit and two values of S for each R.

Data Collection:

No. of Obs.	Direction of Currents	Resistance R  Ω	Shunt resistance S  Ω	Resistance R1  Ω	Galvanometer Deflections	Resistance R1 = RG Ω	Mean RG Ω
01	Direct
	Reverse
02	Direct
	Reverse
03	Direct
	Reverse
04	Direct
	Reverse
05	Direct
	Reverse

Calculation:    Mean Galvanometer resistance  

                            =ohm’s   

                            =               ohm’s

               From equation (3),

              Galvanometer resistance R_G = R₁=   ohm’s

Result: The resistance of a Galvanometer is …………….. Ohm’s

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