A moving coil galvanometer, having a resistance `G`, produces full scale deflection when a current `I_(g)` flows through it. This galvanometer can be converted into
(i) an ammeter of range `0` to `I_(0)(I_(0) gt I_(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)` 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)))R_(A)R_(V)=G^(2)((I_(g))/(I_(0)-I_(g)))`
C. `(R_(A))/(R_(V))=((I_(0)-I_(g))/(I_(g)))^(2)R_(A)R_(V)=G^(2)((I_(0)-I_(g))/(I_(g)))`
D. `(R_(A))/(R_(V))=((I_(g))/((I_(0)-I_(g))))^(2)`

Answer

A

Explanation

Ammeter

`(I_(0)-I_(G))R_(A)=I_(G)G " "(1) implies I_(0)R_(A)=I_(g)(R_(A)+G)`
Voltmenter

`V=I_(g)(R_(v)+G)" "(2)`
`impliesV-I_(g)G=I_(g)R_(V)" "(3)`
`G(I_(0)-I_(g))=I_(g)R_(v)`
`(I_(0)-I_(g))R_(A)=I_(g)G`
Dividing
`G/(R_(A))=(R_(v))/GimpliesR_(v)R_(A)=G^(2)`
From (1) `R_(A)=(I_(g).G)/(I_(0)-I_(g))`
From (3) `R_(v)=(G(I_(0)-I_(g)))/(I_(g))`
`(R_(A))/(R_(v))=(I_(g)^(2))/((I_(0)-I_(g))^(2))`