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

Answer

D

Explanation

In tangent galvanometer number of turns in coil is directly proportional to tangent of deflectoin for tangent galvanometer the number of turns
`N prop tan theta`
hence
`(N_(1))/(N_(2))=(tan theta_(1))/(tan theta_(1))=(tan 60^(@))/(tan 45^(@))=sqrt(3)/(1)`