To know the resistance G of a galvanometer by half deflection method, a battery of emf VE and resistance R is used to deflect the galvanometer by angle   θ.  If a shunt of resistance S is needed to get half deflection then G, R and S are related by the equation :

  • Option 1)

    2S  (R + G) = RG

  • Option 2)

    S ( R + G) = RG

  • Option 3)

    2S = G

  • Option 4)

     2G = S

 

Answers (1)

As we learnt in

Moving coil galvanometer -

It is a very sensitive instrument used to measure the small current.Galvanometer gives the deflection which is proportional to electric current flowing through it.

-

 

 From Ohm's Law  

I= \frac{V}{R}

I_g= \frac{V}{R+G}

where,  Ig = Galvanometer Current

           G = Galvanometer resistance

When shunt of resistance s is connected parallel to the galvanometer then

G=\frac{GS}{G+S}

\therefore I= \frac{V}{R+\frac{GS}{G+S}}

I'_gG= (I-I'_g)S

\Rightarrow I'_g(G+S)= I_s

\Rightarrow I'_g= \frac{I_s}{G+S}

\Rightarrow \frac{I_g}{2}= \frac{I_s}{G+S}

\Rightarrow \frac{V}{2(R+G)}= \frac{V}{R+\frac{GS}{G+S}}\times\frac{S}{G+S}

\Rightarrow \frac{1}{2(R+G)}= \frac{S}{R(G+S)+GS}

After calculate, we get

RG = S(R+G)


Option 1)

2S  (R + G) = RG

This is incorrect option.

Option 2)

S ( R + G) = RG

This is correct option.

Option 3)

2S = G

This is incorrect option.

Option 4)

 2G = S

This is incorrect option.

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