Experiment No: 04
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 RG, 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 Cg is given by
𝑉
Cg =
= kd . . . . . . . . . . . . . . . (1)
𝑅𝐺
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
d
2
, then
C’g = 𝑅
𝑉
𝑑
𝐺 +R1
= k 2 . . . . . .. . . . .. . . (2)
Where C’g is the new galvanometer current.
Dividing (1) by (2), we get
C𝑔
C′g
=
𝑅𝐺 +R1
𝑅𝐺
=
2𝑘𝑑
𝑘𝑑
Or, 𝑅𝐺 + R1 = 2𝑅𝐺
Or, 𝑅𝐺 = R1 . . . . .. . . . . . . . . . . . . (3)
Hence by simply measuring R1, RG 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
Direct
01
Reverse
Direct
02
Reverse
Direct
03
Reverse
04
Direct
Reverse
Direct
05
Reverse
Resistance
R
Ω
Shunt
resistance
S
Ω
Resistance
R1
Ω
Galvanometer
Deflections
Resistance
R1 = RG
Ω
Mean
RG
Ω
Calculation: Mean Galvanometer resistance𝑅𝐺
= Galvanometer resistance R G ÷ 10 ohm’s
=
ohm’s
From equation (3),
Galvanometer resistance RG = R1= ohm’s
Result: The resistance of a Galvanometer is …………….. Ohm’s
Discussions: