To know the resistance G of a galvanometer by half deflection method, a battery of emf V 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?
S(R+G)=RG
2S=G
2S(R+G)=RG
2G=S
Solution:
After applying shunt S, deflection gets halved, hence current gets halved. Hence, (1/2)V/(R+G) = V/(R+G/S) G/(G+S) = (1/2)V/(R+G) Solving this gives S(R+G)=RG.