A galvanometer has a sensitivity of 60 division/ampere. When a shunt is used its sensitivity becomes 10 divisions/ampere. What is the value of shunt used if the resistance of the galvanometer is 20 Ω ?
The sensitivity ratio without and with shunt is 60/10 = 6, indicating that the current through the shunt is 5 times the galvanometer current. Using S = Rg/n-1′ we get S = 20/5 = 4Ω. Hence, the correct answer is (C) 4 Ω.
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Given:
Initial sensitivity = 60 divisions/ampere
Final sensitivity = 10 divisions/ampere
Galvanometer resistance (G) = 20 Ω
The relation is:
S’/S = G/G + S
10/60 = 20/20+S
1/6 = 20/20+S
20 + S = 120 ⟹ S =100Ω
The shunt value is:
S = G×S′/S−S′ = 20×10/60−10 = 4Ω
Answer: (C) 4 Ω
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