Question

Two tangent galvanometers having coils of same radius are connected in series. A current flowing through them produces deflections of ${60}^{\circ }$ and ${45}^{\circ }$ respectively. Find the ratio of the number of turns in the coils.

Answer 1

$I=\frac{2rH}{{\mu }_0{n}_1}tan{60}^{\circ }\left(For{1}^{st}galvanometer\right)$ ...... (1)
$I=\frac{2rH}{{\mu }_0{n}_2}tan{45}^{\circ }\left(For{2}^{nd}galvanometer\right)$ ...... (2)
From (1) and (2), $\frac{2rH\sqrt{3}}{{\mu }_0{n}_1}=\frac{2rH}{{\mu }_0{n}_2}$
$\therefore \frac{n_1}{n_2}=\sqrt{3}:1$