Q. A certain amount of current when flowing in a properly set tangent galvanometer, produces a deflection of $45{^\circ}$. If the current be reduced by a factor of $\sqrt{3}$, the deflection would
A) Decrease by $30{^\circ}$
B) Decrease by $15{^\circ}$
C) Increase by $15{^\circ}$
D) Increase by $30{^\circ}$
Explanation
(b) In tangent galvanometer, $I \propto \tan\theta$
$\therefore\frac{I_{1}}{I_{2}} = \frac{\tan\theta_{1}}{\tan\theta_{2}} \Rightarrow \frac{I_{1}}{I_{1}/\sqrt{3}} = \frac{\tan{45{^\circ}}}{\tan\theta_{2}}$
$\Rightarrow \sqrt{3}\tan{\theta_{2} = 1} \Rightarrow \tan\theta_{2} = \frac{1}{\sqrt{3}} \Rightarrow \ \theta_{2} = 30{^\circ}$
So deflection will decrease by $45{^\circ}$-$30{^\circ} = 15{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.