Question

The certain amount of current when flowing in a properly set tangent galvanometer, produces a deflection of $45^{\circ}$ . 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 $30^{\circ}$

Answer 1

Answer: (B)

decrease by $15^{\circ}$

Answer 2

The correct answer is B:decrease by $15\degree$
When current is passed through tangent galvanometer, a magnetic field is created given by
$B=\frac{\mu_{0} n I}{2 r}$
When it is set in plane, then from tangent law,
$B=B_{H} \tan \theta$
$\Rightarrow \frac{\mu_{0} n I}{2 r}=B_{H} \tan \theta$
$\Rightarrow I=\left(\frac{2 r B_{H}}{\mu_{0} n}\right) \tan \theta$
$\Rightarrow \quad I=K \tan \theta$
where $K$ is reduction factor.
Given $I_{2}=\frac{I_{1}}{\sqrt{3}}, \theta_{1}=45^{\circ}$
$\therefore \frac{I_{1}}{I_{1} / \sqrt{3}}=\frac{\tan 45^{\circ}}{\tan \theta_{2}}$
$\Rightarrow \tan \theta_{2}=\frac{1}{\sqrt{3}}$
$\Rightarrow \theta_{2}=\tan ^{-1}\left(\frac{1}{\sqrt{3}}\right)$
$=30^{\circ}$
Hence, deflection decreases by
$45^{\circ}-30^{\circ}=15^{\circ}$