Two tangent galvanometers A and B have coils of radii `8cm` and `16cm` respectively and resistance `8ohm` each. They are connected in parallel to a cell of emf `4V` and negligible internal resistance. The deflections produced are `30^@` and `60^@` respectivley. A has 2 turns. What is the number of turns in B?

Options

A. 18 turns
B. 12 turns
C. 6 turns
D. 2 turns

Answer

B

Explanation

For a tangent galvanometer, `i = (2rH)/(mu_(0)N) tan theta`
Now 8`Omega` and 8`Omega` in parallel = 4`Omega`.
`i = ("emf")/("resistance") = (4)/(4) = 1` ampere.
`therefore` For T.G . `(r tan theta)/(N) = (mu_(0)i)/(2H)`,
r = radius
`therefore` `(r_(A) tan theta_(A))/(N_(A)) = (r_(B) tan theta_(B))/(N_(B))` or `(r_(A) tan 30^(@))/(N_(A)) = (r_(B) tan 60^(@))/(N_(B))`, N = number of turns
or `(8 xx1)/(sqrt3 N_(A))` = `(16 xx sqrt 3)/(N_(B)) Rightarrow = (8)/(sqrt3 xx 2) = (16 sqrt3)/(N_(B))`
or `N_(B) = 12` turns.