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 `pi` an `R_(A)/R_(v) = I_(g)/(I_(0)- I_(g))`
C. `R_(A)R_(v) = G^(2)` and `R_(A)/R_(v) = (I_(0)/(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_(4) = I_(g)G` and `V_(0) = I_(0)(G + R_(v))`
`I_(0) = (I_(0)(G +R_(A)))/R_(A) V_(0) = I_(0) (G + R_(v))`
`V_(0) = I_(0)G` (Given) `rArr I_(0) (G + R_(V)) = I_(g) (( G+ R_(A))G)/R_(A)`
`R_(v) R_(A) =G^(2)`
`R_(A) = (I_(g)G)/(I_(0)-I_(g)), R_(V) = ((I_(0)-I_(g))G)/I_(g)`
`R_(A)/R_(V) = I_(g)^(2)/(I_(0)-I_(g))^(2)`