MCQ
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 $30^{\circ}$
  • Decrease by $15^{\circ}$
  • C
    Increase by $15^{\circ}$
  • D
    Increase by $30^{\circ}$

Answer

Correct option: B.
Decrease by $15^{\circ}$
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 $45^{-}-30=15$,

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