Answer to Question #98908 in Electric Circuits for Sridhar

Question

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

Answer 1

The current without the shunt:

$$I_1=\frac{V_E}{R+G},$$

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

$$I_2=\frac{V_E}{R+\frac{GS}{G+S}},$$

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

$$I_2=I_1/2.$$

Solve this by equating the currents:

$$S(R+G)+RG$$