Determining Resistance and Figure of Merit with Half-Deflection, Summaries of Physics

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HALF

DEFLECTION

DETERMINATION OF UNKNOWN

RESISTANCE & FIGURE OF MERIT

Demonstrated By: JNYAN RANJAN GURU

DEMONSTRATOR/ LAB INCHARGE, LHTA

AIM OF THE EXPERIMENT

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

APPARATUS REQUIRED

➢ Weston type Galvanometer ➢ A Battery (Battery Eliminator) ➢ High Resistance Box (0- 10000 Ohm’s) ➢ Low Resistance Box (0-200 Ohm’s) ➢ Two One-Way Keys ➢ A Voltmeter (0-3 V) ➢ Connecting Wires ➢ A piece of Sand Paper THEORY ➢ The Resistance of the given Galvanometer as found by half deflection method is given by G=(R×S)/(R-S) ➢ 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) θ ] ➢ Where E is the e.m.f. of the Cell and θ is the deflection produced with resistance R. ➢ The maximum current that can pass through the Galvanometer, Ig=nk ➢ Where n is the total no of division on the Galvanometer scale on either side of zero

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. 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. TABULATION RESISTANCE OF THE GALVANOMETER HIGH RESISTANC E (R) Ohm’s

DEFLECTIO

N (θ) Divisions

SHUNT

RESISTANC

E

(S) Ohm’s

HALF

DEFLECTIO

N

(θ / 2) Divisions

G =

[(RS)

/ (R-

S) ]

Mean Resistance G = (106.8+106.4+106.2+105.8+105.6)/ = 530.8 / 5 = 106.1 Ohm’s

FIGURE OF MERIT OF THE GALVANOMETER

EMF of the Battery = 3.4 V Resistance of Galvanometer (G) = 106.1 Ohm’s n = 30 HIGH RESISTANCE (R) Ohm’s

DEFLECTION

( θ ) K=E/[(R+G)θ] A Div -^1 6100 30 1. 82 × 10-^5 7700 24 1.8 1 × 10-^5 10500 18 1. 78 × 10-^5 13500 14 1. 78 × 10-^5 19000 10 1. 78 × 10-^5 CALCULATION Resistance of the Galvanometer (G) = 106.1 Ohm’s Mean Figure Of Merit k= { (1.82+1.81+1.78+1.78+1.78) × 10

• 5 }/ K= 1.794 × 10
• 5 A Div
• 1 Current required for full scale deflection Ig = nK = 30 × 1.794 × 10
• 5 = 53.82 × 10
• 5