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# In a tangent galvanometer , When a current of $10\;mA$ is passed the deflection is $31^{\circ}$ By what percentage , the current has to be increased , so as to produce a deflection of $42^{\circ}$?

$\begin{array}{1 1} 25\% \\ 30\% \\ 50\% \\ 75\% \end{array}$

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A)
Solution :
Given $I_1= 10\;mA, \theta_1=31^{\circ},\theta _2=42^{\circ}$
$\large\frac{I_2}{I_1} =\frac{\tan \theta_2 }{\tan \theta_2}$
$=> I_2 =I_1\large\frac{\tan \theta_2}{\tan \theta_1}$
$\qquad= 10 \times \large\frac{\tan 42^{\circ}}{\tan 31^{\circ}}$
$\qquad= \large\frac{10 \times 0.9}{0.6}$
$\qquad= 15\;mA$
Percentage increase in current $\large\frac{(I_2-I_1)}{I_1}$
$\qquad =\large\frac{15-10}{10}$$\times 100$
$\qquad= 50\%$
Answer :$50\%$