Two tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of `60^(@)` and `45^(@)` respectively. The ratio of the number of turns in the coils is

Options

A. `4//3`
B. `(sqrt(3)+1)//1`
C. `(sqrt(3)+1)//(sqrt(3)-1)`
D. `sqrt(3)//1`

Answer

D

Explanation

In the first galvanometer
`i_(1)=K_(1) tantheta_(1)=K_(1) tan 60^(@)=K_(1)sqrt(3)`
In the second galvanometer
`i_(2)=K_(2) tan theta_(2)=K_(2) tan 45^(@)=K_(2)`
In series `i_(1)=i_(2)implies K_(1)sqrt(3)=K_(2)impliesK_(1)/K_(2)=1/sqrt(3)`
But `K prop 1/nimplies K_(1)/K_(2)=n_(2)/n_(2) :. n_(1)/n_(2)=sqrt(3)/1`.