Question

Two tangent galvanometers $A$ and $B$ have coils of radii $8cm$ and $16cm$ respectively and resistance $8\Omega$ each. They are connected in parallel with a cell of emf $4V$ 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

Answer: 12

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

From Eq. (i), we get
$\frac{r\tan \theta }{N}=\frac{{\mu }_{0}I}{2B_H}=$ 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