# 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

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.

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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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