Question

To determine the resistance of a moving cell galvanometer by half deflection method

Answer 1

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A method of finding the internal resistance of a cell when the value is known to be high. A second cell, a galvanometer and a resistance are connected in series with the cell under test, and the value of the resistance required to give a galvanometer. deflection of half the value obtained with the cell alone is found.


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Answer 2

One of the main application of half deflection method is to find the resistance of galvanometer

This is the simple circuit diagram for finding the resistance of galvanometer.

In the first condition (when k1 is closed andk2 is open.)

Current i flowing through galvanometer is given by :

i=ER+G ...eqn(1)

Here, R= resistance of H.R.B (high resistance box)

G=resistance of galvanometer

E= EMF of cell.

In moving coil galvanometer

i=kθ …where k=cnab ...eqn(2)

In second condition (when key k1 and key k2 both are closed.)

I=ER+G⋅SG+S...eqn(3)

Now, resistance in L.R.B is maintained in such a way that deflection of galvanometer becomes half.

i.e. I1=θ2 ...eqn(4)

From equation (2) and(4) :

I1=i2 ...eqn(5)

Also I2=I−i2 ...eqn(6)

By the parallel combination of resistances :

I1G=I2S

From equation (5) and(6) :

i2 G=(I−i2)S

Putting value of I1 andI2 from equation (1) and(3)

(E2(R+G)) G=(ER+G⋅SG+S−E2(R+G))S

⟹G2(R+G)+S2(R+G)=S(G+S)R(G+S)+GS

⟹12(R+G)(R+S)=S(G+S)R(G+S)+GS

⟹2(R+G)S=R(G+S)+GS

⟹2(R+G)S=(R+G)S+RG

⟹(R+G)S=RG

⟹RS=RG−SG

⟹G=RS/R−S