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

**Apparatus** : A Weston type of galvanometer , a voltmeter , a battery /battery eliminator , two 10,000 ohm and 200 ohm ) resistance boxes , two one way key , a rheostat , a screw gauge , a meter scale , an ammeter of given range , connecting wires and a piece of sand paper .

**Theory **

The resistance of the given galvanometer as found by half deflection method .

G= (RxS)/(R-S) (1)

Where R is the resistance connected in series with the galvanometer and S is the shunt resistance .

The figure of merit , K =E /[(R+G)Q] (2)

Where E is the end of the cell and Q is the deflection produced with resistance R.

The maximum current that can pass through the galvanometer , I_{g}=nk

Where n is the total number of dimension on the galvanometer scale on either side of zero .

**Procedure **

1. Resistance of galvanometer by half deflection method

- Make the connections accordingly as shown in circuit diagram .
- See that all plugs of the resistance boxes are tight
- Take out the high resistance (200 Ohm ) from the resistance box R and insert key K1 only .
- Adjust the value of R1 so that deflection is maximum , even in number and within the scale .
- Note the deflection . Let it be Q.
- Insert the key k2 also and without changing the value of R2 ,adjust the value of S , such that deflection in the galvanometer reduces to exactly half the value of resistance S.
- Note the value of resistance S .
- Repeat step 4 & 7 three times taking different R and adjusting .

2. Figure of merit

- Take one cell of the battery and find its emf by a voltmeter by connecting +ve of the voltmeter with +ve of cell and – ve of the voltmeter with -ve of cell . Let it be E.
- Take connection as in circuit diagram .
- Adjust the value of R to obtain a certain deflection Q when circuit is closed .
- Note the value of resistance R and deflection Q.
- Now change the value of R and note the galvanometer deflection again .
- Repeat the step with both cells of the battery with different voltages like 2,4,6 ,8 volts from battery eliminator.
- Find the figure of merit K using the formula

**Observation table **

Resistance (R) | Deflection (Q) | Shunt (S) | G =(RxS)/(R-S) |

5000 | 10 | 5 | 5.005 |

10000 | 6 | 3 | 3 |

2000 | 20 | 10 | 10.05 |

1500 | 26 | 3 | 13.11 |

Average | G = 7.79 ohms |

Resistance (R) | Deflection (Q) | K |

5000 | 9 | 0.556 |

10000 | 5 | 0.60 |

2000 | 20 | 0.502 |

1500 | 25 | 0.524 |

Average | K = 0.5455 A/dn |

** Calculations**

- G = (5.005+3+10.05+13.11)/4 [E = 1.45V]
- Figure of Merit : Current in the galvanometer per unit time
- K = IQ = [(E)/(R+G)]x[1/Q] – SI unit = AD division = 10
^{-5}Al div

**Result **

Resistance of given galvanometer is 7.79 ohm .

Figure of merit of given galvanometer is 0.545 A/dn .

**Precautions **

All connections should be neat and tight .

The emf of cell / battery should be constant .

**Source of error **

The scene of the instrument may be loose .

The galvanometer division may not be of equal size.

**Diagram**

**Resistance of Galvanometer**

**Figure of Merit**

**Viva question **

What is the galvanometer ?

It is a device used for detecting feeble electric currents in circuit .

Define the figure of merit of a galvanometer ?

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

Why is this method called half deflection method ?

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

Under what condition id the resistance of a galvanometer (E_{1}) equal to shunt resistance (S)?

E1=S , only when series resistance R is very high .

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