Experiment 4: 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 :
Connect the galvanometer whose resistance is to be determined in series with a high resistance R as shown in Fig. 2.5.
Close key K₁, keeping key K₂ open. If I current pass through the galvanometer,
Then
$I_g = \frac{E}{R+G}$
If $\theta$ is the deflection produced in the galvanometer, then
$\frac{E}{R+G} = k\theta \quad \ldots \text{(i)}$
Now key $K_2$ is closed and shunt S is so adjusted that the deflection is $\frac{\theta}{2}$
If $I_g'$ is the current flowing through the galvanometer at this stage, then
$I_g' = \frac{k\theta}{2} \quad \ldots \text{(ii)}$
At this stage, total resistance in the circuit
$R' = R + \frac{GS}{G+S}$
Total current in the circuit,
$I = \frac{E}{R'} = \frac{E}{R + \frac{GS}{G+S}} \quad \ldots \text{(iii)}$
So, the current through the galvanometer
$I_g' = I \left(\frac{S}{S+G}\right)$
Using eq (iii), we get
$I_g' = \frac{E}{R + \frac{GS}{G+S}} \times \frac{S}{G+S}$
$I_g' = \frac{ES}{R(G+S) + GS}$
Using eq (ii)
$\frac{ES}{R(G+S) + GS} = \frac{k\theta}{2} \quad \ldots \text{(iv)}$
Dividing (i) by (iv), we get
$\frac{R(G+S) + GS}{(R+G)S} = 2$
or
$RG + RS + GS = 2RS + 2GS$
$RG - GS = RS$
or
$G = \frac{RS}{R-S} \quad \ldots \text{(v)}$
Figure of merits (k) :
It is the current required to produce a deflection of one division on the galvanometer, so it is also called the sensitivity of the galvanometer.
Note the deflection $\theta$ in the galvanometer the current I flowing through the circuit
$I = \frac{E}{R+G}$
$k = \frac{I}{\theta} = \frac{E}{\theta(R+G)}\quad \ldots \text{(vi)}$
Procedure :
- Draw the diagram as shown in Fig. 2.5 and arrange the apparatus according to the circuit diagram.
- Introduce a high resistance R from the resistance box and insert key $K_1$. Adjust the value of R to get almost full scale deflection in the galvanometer. Note the value of R and $\theta$.
- Close key $K_2$ keeping R fixed, adjust the value of S so that the deflection is half (i.e. $\frac{\theta}{2}$)of previous value. Note the value of S.
- Repeat the experiment three times for different values of the resistance from the resistance box R.
Figure of merit :
- Measure the e.m.f. of the battery using an accurate voltmeter. Let it be E.
- Put the plug in the key $K_1$ and introduce resistance R (key $K_2$ is not closed). Note the deflection \theta in the galvanometer.
- The figure of merit, $k = \frac{\text{E}}{(\text{R} + \text{G})\theta}$.
Observations :
Calculations:
Precautions :
1. All connections must be neat and tight
2. Key $K_1$ should be closed after taking out a high resistance from the resistance box R.
3. Ammeter should always be connected in series.
4. The deflection of galvanometer should be large.
5. Positive terminal of the ammeter should be connected to the positive pole of the battery.
Sources of Error
1. The e.m.f. of the battery may vary.
2. The galvanometer scale may not be equally spaced.
VIVA VOCE :
Q. 1. What is a galvanometer?
Ans. It is a low resistance instrument used to detect the presence of an electric current in
Q. 2. What do you mean by shunt?
Ans. A shunt is a small resistance connected in parallel to an electrical instrument like galvanometer in the circuit so that only a very small portion of the total current passes through the galvanometer.
Q. 3. Is the thickness of all the wires inside a resistance box the same ?
Ans. No, the thickness is not same.
Q. 4. When the shunt is increased, will the deflection in the galvanometer increase or decrease?
Ans. The deflection through the galvanometer will increase because when the shunt is increased, the current through
Q. 5. Define figure of merit of a galvanometer.
Ans. It is defined as the current required to produce a deflection of one scale division in the galvanometer.
Q. 6. What is the difference between a galvanometer and an ammeter?
Ans. An ammeter is a low resistance galvanometer which gives the value of the current to be measured directly in amperes.
Q. 7. Can we increase or decrease the range of an ammeter?
Ans. Yes, the range of the ammeter can be increased or decreased by shunting it with a low or high resistance of the
Q. 8. What is a voltmeter?
Ans. A voltmeter is a galvanometer which measures the value of the potential difference between two points directly.
Q. 9. Why is it necessary for a voltmeter to have a high resistance?
Ans. A voltmeter is connected in parallel in the circuit. If it has a low resistance it will reduce the value of actual
Q. 10. Can we increase the range of a voltmeter?
Ans. Yes, the range of a voltmeter can be increased by adding extra resistance is series with the voltmeter.
Q. 11. What is the resistance of an ideal voltmeter?
Ans. An ideal voltmeter has infinite resistance so that it draws no current in the circuit.
Q. 12. What type of galvanometer is Weston type galvanometer?
Ans. It is a moving coil galvanometer.
Q. 13. What is the unit of figure of merit?
Ans. Its unit is ampere per division.
Q. 14. What is the order of resistance of the galvanometer we use?
Ans. For Weston galvanometer, it is of the order $20 \Omega$.
Q. 15. What are the types of galvanometer?
Ans. Galvanometers are moving magnet type or moving coil type galvanometer. They are further divided as dead
Q. 16. Which type of galvanometer, we use in this experiment?
Ans. It is Weston type dead beat galvanometer.
Q. 17. What is the value of $I_g$ and G in your galvanometer?
Ans. In general, $I_g = 600 \muA$ and $G= 60 \Omega$.
Q. 18. Why a moving coil galvanometer so called?
Ans. Because the coil moves while the magnet remains fixed.
Q. 19. What is the principle behind moving coil galvanometer?
Ans. It is based on the principle that when a current carrying coil is placed in external magnetic field, it experiences a torque = n I A B.
Q. 20. Can a galvanometer measure alternate current?
Ans. No.
