A moving coil galvanometer, having a resistance G, produces full scale deflection when a current Ig flows through it. This galvanometer can be converted into
(i) An ammeter of range 0 to `I_(0)(I_(0)gtI_(g))` by connecting a shunt resistance `R_(A)` to it and
(ii) Into a voltmeter of range 0 to `V(V=GI_(0))` by connecting a series resistance `R_(V)` to it. Then

Options

A. `R_(A)R_(V) = G^(2)((I_(0)-I_(g))/I_(g))` and `R_(A)/R_(V) =(I_(g)/(I_(0)-I_(g)))^(2)`
B. `R_(A)R_(V) = G^(2)` and `R_(A)/R_(V) = I_(g)/(I_(0)-I_(g))`
C. `R_(A)R_(V) = G^(2)` and `R_(A)/R_(V) =I_(g)/(I_(0)-I_(g))^(2)`
D. `R_(A)R_(V) = G^(2)(I_(g))/(I_(0)-I_(g))` and `R_(A)/R_(V) =((I_(0)-I_(g))/I_(g))^(2)`

Answer

C

Explanation

`(I_(0)-I_(G))R_(A) = I_(G)G` and `V_(0) = I_(G)(G + R_(V))`
`I_(0) = (I_(G)(G + R_(A)))/R_(A), V_(0) = I_(G)(G +R_(V))`
`R_(A)G + R_(V)R_(A) = G^(2) +R_(A)G`
`R_(V)R_(A) = G^(2)`
`R_(A)G + R_(V)R_(A) = G^(2) + R_(A)G`
`R_(A)/R_(V) = I_(G)^(2)/(I_(0)-I_(G))^(2)`