Question

Two tangent galvanometers $A$ and $B$ have coils of radii $8\,cm$ and $16\,cm$ respectively and resistance $8 \, \Omega$ each. They are connected in parallel with a cell of emf $4\,V$ and negligible internal resistance. The deflections produced in the tangent galvanometers $A$ and $B$ are $30^\circ \, $ and $\, 60^\circ $ respectively. If $A$ has $2$ turns, then the number of turns $B$ must have is

Answer 1

Current in tangent galvanometer
$I=\frac{2 r B_{H}}{\left(\mu \right)_{0} N}\tan \theta \, \, ..\left(i\right)$

From Eq. (i), we get
$ \, \, \frac{r \tan \theta }{N}=\frac{\mu _{0} I}{2 B_{H}}=$ same for both
$\therefore \, \frac{r_{A} \tan \theta _{A}}{N_{A}}=\frac{r_{B} \tan ⁡ \theta _{B}}{N_{B}}$
$\Rightarrow \, \, \, \frac{8 \times 1}{\left(2\right) \sqrt{3}}=\frac{16 \sqrt{3}}{N_{B}}$
$\therefore \, \, \, N_{B}=12 \, $ turns