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((Ig)/(I_0-I_g))`
C. `R_A/R_V=((I_0-I_g)/I_g)^2`
D. `R_A/R_V=((I_g/((I_0-I_g))^2 R_A R_V=G^2((I_0-I_g)/I_g)`

Explanation

Ammeter
`(I_0-I_G)R)A-I_G G`
(1) `implies I_0R_A=I_g(R_A+G)`
Voltmeter
`V=I_g(R_v+G) (2)`
`implies V-I_gG=I_gR_v` (3)
`G(I_0-I_g)=I_gR_v (J_0-I_g)R_A=I_g G`
Dividing
`G/R_A=R_v/G Implies R_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`