CLASS 12TH PHYSICS EXPERIMENT To determine resistance of a galvanometer by half deflection method and to find its figure of merit.

To determine resistance of a galvanometer by half deflection method and to find its figure of merit.

Aim:
To determine resistance of a galvanometer by half deflection method and to find its figure of merit.
Apparatus:
Moving coil galvanometer , two resistance boxes , two one way keys , connecting wires , sand paper and a battery.
Theory:
To find resistance of galvanometer (G)
Galvanometer of resistance G when connected in series with a resistance R and a battery of emf E , the current is I=E/(R+G) if 𝚹 is the deflection.

K𝚹 = E/(R+G) 

Now such a resistance S is connected in parallel with G , that the deflection becomes half i e 𝚹/2, then 

  K(𝚹/2) = E/(R + (GS/(G+S))

Using K𝚹 in this we have

E/(R+G)2 = E(G+S) / R (G + S ) + GS , on solving

G = RS/ (R-S)

Half deflection method Class 12th Physics Practical

To find figure of merits (k)

Figure of merit is current per unit deflection i e , 

k=I/𝚹

k=I/𝚹=E/(R+G)𝚹

Procedure: 

a)To find resistance of galvanometer (G)

1. Make connection according to the circuit diagram given above.
2. Connect a battery B , galvanometer G , resistance box R and a key K , in series.
3. Connect another resistance box S and a key K2 parallel with the galvanometer.
4. Take out 5000 Ω plug from resistance box R , close key K1 . Change the value of R so that deflection in the galvanometer is a little less than full scale deflection but even number of division. Note the deflection and also the resistance R.
5. Take out 50 Ω plug from resistance box S , close the key K2  , adjust the value of S so that the deflection is half of that obtained in step 4 . Note the value of deflection.
6. Repeat set 4 and 5 for more set of reading.

b) To find figure of merits (k)

1. Note least count of voltmeter and see that its zero error is nil. Take out battery from the circuit and measure its emf by using voltmeter let it be E.
2. Now join the battery again in the circuit and plug in key K1 and introduce resistance R (key K2 is not closed. Note the deflection 𝜭 in the galvanometer.
3. Find figure of merits (k) by using 

k=I/𝚹=E/(R+G)𝚹

Observation and calculations:

a) Resistance of Galvanometer (G) by Half deflection method:

S. No.	Resistance R(Ω)	K1 is closed deflection θ	Shunt resistance S(Ω)	K1 and K2  is closed Half deflection θ/2	G= RS/(R-S) Ω
1	7500	24	12	120	121.95
2	10000	18	9	107	108.15
3	15000	12	6	120	120.96
4	19000	10	5	130	130.89
5	13000	14	7	115	116.03

Mean value of G = (121.95+108.15+120.96+130.89+116.03)/5=119.60Ω

b) Figure of merit (k)

Least count of voltmeter= 0.1 V

Range of voltmeter = 5 V

Zero error of voltmeter = nil

S. No.	E M F of battery	Resistance R(Ω)	K1 is closed deflection θ	k= E/(R+G)θ  in (A/div)
1	2	7500	24	1.10 x 10-5
2	2	9000	20	1.10 x 10-5
3	2	9900	18	1.12 x 10-5
4	2	15000	12	1.11 x 10-5

Mean value of k =1.11 x 10^-5  A/div

Result:

The resistance of galvanometer(G) by half deflection method =  119.60 Ω

Figure of merit of galvanometer = 1.11 x 10^-5  A/div

Precautions:

1. All connections must be neat and tight
2. Key K1 should be closed after taking out a high resistance from the resistance box R.
3. The deflection of galvanometer should be large.

Sources of error:

1. The emf of battery may vary.
2. The galvanometer scale may not be equally spaced.
3. Loose plugs cause an error.