Answer to Question #98908 in Electric Circuits for Sridhar

Question #98908
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 :
(1)2S(R+G)=RG
(2)S(R+G)=RG
(3)2S=G
(4)2G=S
1
Expert's answer
2019-11-20T09:42:19-0500

The current without the shunt:


I1=VER+G,I_1=\frac{V_E}{R+G},

The current with the shunt (it is parallel to the galvanometer):


I2=VER+GSG+S,I_2=\frac{V_E}{R+\frac{GS}{G+S}},

and this current is twice as small as the current in the first case:


I2=I1/2.I_2=I_1/2.

Solve this by equating the currents:


S(R+G)+RGS(R+G)+RG


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