Two tangent galvanometers, which are identical except in their number of turns are connected in parallel. The ratio of their resistances of the coils is `1 : 3`. If the deflections in the two tangent galvanometers are `30^(@)` and `60^(@)` respectively, then the ratio of their number of turns is

Options

A. `1 : 1`
B. `3 : 1`
C. `1 : 2`
D. `1 : 9`

Explanation

For a tanget galvanometer
`I= (2r B_(H) tan theta)/(n mu_(0))`
where r is the radius of the coil and n is the number of turns
For tangent galvanometer 1
`I_(2) = (2rB_(H))/(n_(1) mu_(0)) tan 30^(@)`
For tangent galvanometer 2
`I_(2) = (2rB_(H))/(n_(2)mu_(0)) tan 60^(@)`
As they are connected in parallel,
`:. V_(1) = V_(2)`
`I_(1) R_(1) = I_(2)R_(2)`
`(2rB_(H) tan 30^(@))/(n_(1) mu_(0)) R_(1) = (2rB_(H) tan 60^(@))/(n_(2) mu_(0)) R_(2)`
`:. (n_(1))/(n_(2)) = (R_(1))/(R_(2)) (tan 30^(@))/(tan 30^(@)) = (1)/(3) (tan 30^(@))/(3 tan 60^(@)) = (1)/(9) " " ( :' (R_(1))/(R_(2)) = (1)/(3) ("Given"))`
None of the given options is correct