To Determine Resistance of A Galvanometer by Half-Deflection Method And To Find Its Figure of Merit

Table of Contents

Aim/Aim of Experiment

To determine Resistance of a Galvanometer by Half-Deflection Method and To find Its Figure of Merit.

Apparatus/Material Required

A Battery (Battery Eliminator)
A Weston Type Galvanometer
A Voltmeter
An Ammeter
Two Resistance Boxes (10K ohm & 200 ohm)
Two One-way Keys
A Rheostat
A Screw guage
A Meter Scale
Connecting wires
A piece of Sand paper.

Theory

1. The Resistance of the given Galvanometer as found by half deflection method is given by G=(R×S)/(R-S) (Eq. 1)

where R is the resistance connected in series with the Galvanometer and S is the Shunt resistance.

2. The Figure of Marit, k=E/[(R+G)θ] (Eq. 2)

where E is the e.m.f. of the Cell and θ is the deflection produced with resistance R.

3. The maximum current that can pass through the Galvanometer, I_g=nk (Eq. 3)

where n is the total no of dimension on the Galvanometer scale on either side of zero.

Circuit Diagram

to determine resistance of a galvanometer by half-deflection method and to find its figure of merit — Circuit Diagram of Resistance of Galvanometer & Figure of Merit

Procedure

Resistance of Galvanometer by Half-Deflection Method:
1. Connect the Apparatus and make the connection as shown in circuit diagram.
2. Ensure that all the plugs in the resistance boxes should be tight.
3. Now Take out the high resistance (say 2000 Ω) from the resistance box R and insert the key K1 only.
4. Adjust the value of R so that deflection is maximum, even in number and within the scale.
5. Note the deflection (say θ).
6. Now insert the key K2 without changing the value of R. Adjust the value of S, such that the value of the deflection reduces to exactly half the value obtained which is half of θ, (Step 5) i.e. θ/2.
7. Note down the value of resistance S.
8. Repeat steps 4 to 7 three times taking out different values of Resistance (R) and adjusting the Shunt resistance (S) every time.
Figure of Merit:
1. Take one cell of the battery (battery eliminator) and find its E.M.F. by a voltmeter by connecting +ve of the voltmeter with +ve of the cell and -ve of voltmeter with -ve of the cell, (Say E).
2. Make connections as in circuit diagram.
3. Adjust the value of R to obtain a certain deflection 0 (say 30 divisions) when the circuit is closed.
4. 12.Note down the values of resistance R and deflection θ.
5. Now change the value of R and note the Galvanometer deflection again and note it.
6. Repeat the (Figure of Merit) steps 1 to 5 with both cells of the battery with different voltages like 2, 4, 6, 8, volts from Battery eliminator.
7. Now find the figure of merit k using the formula.

Observations

1. Table for Resistance of the Galvanometer by half-deflection method:

Serial No. of Obs. (1)	Resistance R (ohm) (2)	Deflection in the Galvanometer θ (3)	Shunt Resistance S (ohm) (4)	Half Deflection θ/2 (5)	Galvanometer Resistance G=(R×S)/(R-S) (ohm) (6)
1.	3300	30	80	15	81.9
2.	5000	20	80	10	81.3
3.	10900	10	80	5	80.5
4.	12700	8	80	4	80.1

Table 1

2. Table for Figure of Merit:

Serial No. of Obs. (1)	No. of Cells (Battery Eliminator) (2)	EMF of the Cells E(V) (3)	Resistance from R.B. R (ohm) (4)	Deflection θ (div.) (5)	Figure of Merit k=E/[(R×G)θ] (6)
1.	1	2	5000	20	1.9×10^-5
2.	2	4	10,000	20	1.9×10^-5
3.	3	6	15,000	20	1.9×10^-5
4.	4	8	10,000	20	1.9×10^-5

Table 2

No. of divisions in the Galvanometer scale, n = 30.

Calculations

Calculation for G:
- Calculate G, using formula G=(R×S)/(R-S) and write it in column 6 of Table 1.
- Take mean of value of G recorded in column 6 of Table 1.
Calculation for k:
- Calculate k, using formula k=E/[(R×G)θ] and write it in column 6 of Table 2.
- Take mean of value of k recorded in column 6 of Table 2.

Result

The resistance of the given galvanometer = 81.09 Ω.
The Figure of Merit of a given Galvanometer = 1.9×10^-5 A/dn.

Precutions

All the connections should be neat, clean and tight.
All the plugs in the resistance box and screw of the instruments should be tight.
The e.m.f. of Cell or Battery eliminator should be constant.
The Galvanometer division must be in equal size.
Initially a high resistance from the resistance box (R) should be introduced in the circuit (otherwise for small resistance an excessive current will flow through the galvanometer or ammeter can be damaged).

Sources of Error

The Screws of the instruments may be loose.
The plugs of Resistance boxes may not be clean.
The e.m.f. of Battery may not be constant.
The Galvanometer divisions may not be of equal size.

Viva Voice Questions with Answers

1. What is a galvanometer?

Answer: It is a device (instrument) used for detecting feeble electric currents in circuits.

2. What type of galvanometer is available in laboratories?

Answer: The laboratory galvanometer is a Weston Galvanometer. It has a pivoted coil.

3. Why the scale of galvanometer has zero in the middle?

Answer: A needle at zero in the middle can deflect on both sides.

4. Do we have positive and negative terminal in a Galvanometer?

Answer: No, a galvanometer has no positive and negative terminals. The pointer can deflect on either side from zero in the middle.

5. Why the divisions of a galvanometer scale are equally spaced?

Answer: Deflection in pointer is proportional to the current passed. The number of divisions in deflection will be proportional to the current passed. I ∝= ∅.

6. Define figure of merit of a galvanometer.

Answer: The quantity of current required to produce a deflection of one division in the galvanometer, is called figure of merit of the galvanometer. It is represented by the symbol k. Its unit is ampere per division.

7. Define current sensitivity of a galvanometer.

Answer: The deflection produced in the galvanometer when a unit current is passed through it, is called current sensitivity of the galvanometer.

8. How are ‘Figure of Merit’ and ‘Current Sensitivity’ related to each other?

Answer: They sire reciprocal, S₁∝ 1/k.

9. What do you mean by resistance of a galvanometer?

Answer: The resistance of the coil of a galvanometer, is called the resistance of the galvanometer. It is represented by the symbol G.

10. How do you determine the resistance of a galvanometer?

Answer: The resistance of a galvanometer is determined by half-deflection method.

11. Why is this method called half-deflection method?

Answer: It is so because the deflection is made half by using a shunt resistance S.

12. Under what conditions, G = S?

Answer: G = S, only when series resistance R is very high.

13. What is the order of resistance of a voltmeter?

Answer: The voltmeter resistance is of the order of series high resistance (R is in ten thousands, G is in hundreds).

14. What is shunt? State its S.l. unit.

Answer: A small resistance connected in parallel with a galvanometer is called shunt. Its S.l. unit is olim.

15. What do you mean by the resistance of a galvanometer?

Answer: The resistance offered by the coil of galvanometer to the flow of current through it is known as resistance (G) of the Galvanometer.

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