• # question_answer The tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of $60{}^\circ$ and $45{}^\circ$ respectively. The ratio of the number of turns in the coil is: A) (4/3) B) $(\sqrt{3}+1)/1$ C) $\left( \frac{\sqrt{3}+1}{\sqrt{3}-1} \right)$ D) $\sqrt{3}/1$

 For tangent galvanometer $\frac{\mu NI}{2R}={{B}_{H}}\tan \theta$ $\therefore \,\,\frac{{{N}_{1}}}{{{N}_{2}}}=\frac{\tan {{\theta }_{1}}}{\tan {{\theta }_{2}}}\Rightarrow \frac{{{N}_{1}}}{{{N}_{2}}}=\frac{\tan 60{}^\circ }{\tan 45{}^\circ }=\frac{\sqrt{3}}{1}$