A galvanometer of resistance `GOmega`, is shunted by a resistance `S Omega`. To keep the main current in the circuit unchanged, the resistance to be connected in series with the galvanometer is

Options

A. `G^(2)/(S+G) `
B. `S/(S+G)`
C. `S^(2)/(S+G)`
D. `(SG)/(S+G)`

Answer

A

Explanation

Given, galvanometer resistance, `R_(G) = G` and shunt resistance, `R_(S) = S`,
Let the series resistance is R, so the net resistance of circuit after connected R,
`R_(0) = R + (G xx S)/(G+R)" "...(i)`
Since, it is given that the current should not change. So it should be G,
`R_(0) = G" "...(ii)`
From Eq. (i) and (ii), we get
`G = R + (GxxS)/(G+S)`
`rArr R = G - (GS)/(G + S) rArr R = G^(2) / (G + S)`
Hence, the correct option is (a).