To Determine Resistance Of A Galvanometer By Half-deflection Method And To Find Its Figure Of Merit. - Practice Questions & MCQ

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

Apparatus
A Weston type galvanometer, a voltmeter, a battery or battery eliminator, two resistance boxes $(10,000 \Omega$, and $200 \Omega)$, two one-way keys, a rheostat, a screw gauge. a meter scale, an ammeter of the given range, connecting wires and a piece of sandpaper.

Theory
(i) The resistance of the given galvanometer as found by half deflection method

$
G=\frac{R \cdot S}{R-S} \ldots \ldots
$

where $R$ is the resistance connected in series with the galvanometer and $S$ is the shunt resistance.
(ii) The figure of merit

$
k=\frac{E}{(R+G) \theta} \ldots
$

where E is the e.m.f. of the cell and $\theta$ is the deflection produced with resistance R
(iii) The maximum current that can pass through the galvanometer,

$
i_g=n k
$

where n is the total number of divisions on the galvanometer scale on either side of zero.

Circuit Diagram-

Procedure: 

(a) The resistance of a galvanometer by half deflection method
1. Make the connections accordingly as shown in the circuit diagram.
2. See that all plugs of the resistance boxes are tight.

3. Take out the high resistance (say $2000 \Omega$ ) from the resistance box $R$ and insert the key $\mathrm{K}_1$ only.
4. Adjust the value of $R$ so that deflection is maximum, even in number and within the scale.|
5. Note the deflection. Let it be $\theta$.
6. Insert the key also and without changing the value of R, adjust the value of S, such
$\frac{\theta}{2}$
that deflection in the galvanometer reduces to exactly half the value obtained in step 5 i.e., $\overline{2}$
7. Note the value of resistance $S$
8. Repeat steps 4 to 7 three times taking out different values of $R$ and adjusting $S$ every time.
(b) Figure of merit
9. 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. Let it be E. 10. Make connections as in the circuit diagram.
11. Adjust the value of $R$ to obtain a certain deflection 0 (say 30 divisions) when the circuit is closed.
12. Note the values of resistance R and deflection $\theta$.
13. Now change the value of $R$ and note the galvanometer deflection again.
14. Repeat the steps 9 to 13 with both cells of the battery with different voltages like 2,4,6,8 volts from battery eliminator.
15. Find the figure of merit $k$ using the formula.

Calculations
Calculation for G
1. Calculate $G$ using

$
G=\frac{R \cdot S}{R-S}
$

2. Calculate the mean value of G

Calculation for k

1. Calculate k using 

$
k=\frac{E}{(R+G) \theta}
$

2. Calculate the mean value of $k$

Result
1. The resistance of given galvanometer $=\ldots \Omega$
2. The figure of merit of given galvanometer = $\qquad$ Ampere per division