When $\sqrt 3$ ampere current is passed in a tangent galvanometer, there is deflection of ${30^0}$in it. The deflection obtained when 3 amperes current passed is ?
A. ${30^0}$
B. ${45^0}$
C. ${60^0}$
D. ${75^0}$

Hint: First try to find out what is the relationship between the current and the deflection angle that is the tangent of the angle of deflection in case of the tangent galvanometer. Then put all the required value from the information provided in the question above and finally you will get the required angle of deflection at the 3 amperes current.

Formula used:
The relation between current and deflection of a tangent galvanometer is,
$i \propto \tan \theta $
Where, i is current and $\tan \theta $ is the tangent of the angle of deflection.

Complete step by step solution:
In case of tangent galvanometer,
We know that:
Current is directly proportional to the tangent of the angle of deflection,
$i \propto \tan \theta $...........(Equation 1)
Now, from the question we have;
${i_1} = \sqrt 3 $
$\Rightarrow {i_2} = 3$
$\Rightarrow {\theta _1} = {30^0}$
Now using the equation 1, we get;
$\dfrac{{\sqrt 3 }}{3} = \dfrac{{\tan {\theta _1}}}{{\tan {\theta _2}}} = \dfrac{{\tan {{30}^0}}}{{\tan {\theta _2}}} \\ $
After solving we get;
$\therefore \theta = {45^0}$

Hence the correct answer is option B.

Note: Here angle of deflection is asked in case of a tangent galvanometer so the current was directly proportional to the tangent of the angle of deflection but if the tangent galvanometer is replaced by a simple galvanometer then the current will be directly proportional to the angle of the deflection then the answer will get changed.