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A certain amount of current when flowing in a properly set tangent galvanometer, produces a deflection of $45^{o}$ . If the current be reduced by a factor of $\sqrt{3}$ , the deflection would

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Increase by $15^{o}$

Decrease by $15^{o}$

Increase by $30^{o}$

Decrease by $30^{o}$

answer is B.

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Detailed Solution

In tangent galvanometer, $I \propto \tan θ$

$∴ \frac{I_{1}}{I_{2}} = \frac{\tan θ_{1}}{\tan θ_{2}} \Rightarrow \frac{I_{1}}{I_{1} / \sqrt{3}} = \frac{\tan 45^{o}}{\tan θ_{2}}$

$\Rightarrow \sqrt{3} {tanθ}_{2} = 1 \Rightarrow {tanθ}_{2} = \frac{1}{\sqrt{3}} \Rightarrow θ_{2} = 30^{o}$

So deflection will decrease by $45^{o} - 30^{o} = 15^{o}$

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