Question

When $\sqrt{3}\text{A}$ current is passes through a tangent galvanometer, there is a deflection of ${30}^{\circ }$ in it. The deflection obtained when $3\text{A}$ current passing through it-

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${60}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is B ${45}^{\circ }$

In the tangent galvanometer, the magnetic needle comes to an equilibrium, when

$B_{coil}=B_H\tan \theta$

$\Rightarrow \frac{N\mu i}{2r}=B_H\tan \theta$

$\Rightarrow i\propto \tan \theta$

$\frac{i_2}{i_1}=\frac{\tan {\theta }_2}{\tan {\theta }_1}$

$\tan {\theta }_2=\sqrt{3}\tan {30}^{\circ }$

$\tan {\theta }_2=1\Rightarrow \theta ={45}^{\circ }$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.