To determine the resistance of a galvanometer by Half-deflection Method by Yasir Own's

To determine the resistance of a galvanometer by Half-deflection Method an to Find its Figure of Merit

Introduction:

In this physics project, we explore the concept of measuring the resistance of a galvanometer using the half deflection method and calculating its figure of merit. A galvanometer is essential instrument for detecting and measuring small electric currents. By understanding its resistance and sensitivity, we gain insights into this precision and suitability for various applications. Through a hands-on experimental approach, we will determine the galvanometer's resistance and explore its figure of merit, providing a deeper understanding of its functionally in electrical measurment.

Body Part/Experiment:

Aim:

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

Appartus Required:

• A moving coil galvanometer
• A bettery
• 2 one way keys
• Voltmeter
• Connecting Wires
• 1 High Resistance Box
• 1 Low Resistance Box
• A piece of Sand Paper
• A Screw Gauge
• Ammeter

Theory:

The resistance of the given galvanometer as found by half defection method is $\begin{array}{l}G=\frac{R\times S}{R-S}\end{array}$
where R is the Resistance connected in Series with the galvaometer and S is the Shunt Resistance.

The figure of merit,$\begin{array}{l}K=\frac{E}{(R+G)\theta }\end{array}$
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 number of dimensions on the galvanometer scale on either side of zero.

Procedure:

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, and note the deflection θ.
• Insert the the key K2 also and without changing the value of R2, adjust the value of Sand note it down.
• Repeat steps 4 & 5 four times taking different R and adjusting.




Figure of Merit:

• Take one cell of the battery and find its emf by a voltmeter by connecting +ve of the voltmeter with +ve pf the cell and -ve of the voltmeter with -ve of cell. Let it be E.
• Take connections as in Circuit diagram.
• Adjust the value of R and note the galvanometer deflection again.
• Repeat the steps with both cells of the battery with constant voltage from battery eliminator.
• Find the figure of Merit using the formula.




Observation:

Resistance for Galvanometer:



Figure of Merit:




Calculation:

The mean Value for G is = ( 103.2+103+103.6+105.6)/4
G = 103.8 Ω.

The mean Value for K is = {( 1.61+1.59+1.54+1.59 )x10^-5}/4
K = 1.58x10^-5 amp/div.

Result:

The resistance of the given galvanometer = 103.8 Ω.
The figure of merit of a given galvanometer = 1.58x10^-5 A/dn.

Precautions:


• Key K1 should be inserted only after high value of R has been taken out from resistance box otherwise galvanometer coil may burn.


• Adjust R such that deflection in galvanometer is of even division so that θ/2 is more conveniently obtained.


• Emf of the battery should be constant.


• Use as high values of R as practically possible. This ensures correct value of G.


• All the connections and plugs in the resistance box should be tight.


Sources of Error:


• Plugs in the resistance boxes may be loose or they may not be clean.


• The emf of the battery may not be constant.


• The galvanometer may not be of equal size.

Conclusion:

Through the half deflection method, we successfully determined the resistance of the galvanometer and calculated its figure of merit. The experiment showcased the galvanometer's sensitivity to small currents and its precision in measuring electrical quantities. We observed how the shunt resistance plays a crucial role in preventing excessive current flow through the galvanometer. By understanding the galvanometer's resistance and figure of merit, we gained valuable insights into its applicability in various electrical measurements, enhancing our understanding of this essential instrument.