Question

A tangent galvanometer properly adjusted gives a deflection of 30${}^o$ when a certain current is passed through it. When the current is changed,then it gives a deflection of 45${}^o$. The ratio of the currents in the two cases is :

• A. 2 : 3
• B. $1:\sqrt{2}$
• C. $1:\sqrt{3}$
• D. $\sqrt{3}:1$

Answer 1

The correct option is C $1:\sqrt{3}$

$\frac{i_1}{i_2}=\frac{\tan {\theta }_1}{\tan {\theta }_2}$
or, $\frac{i_1}{i_2}=\frac{\tan {30}^0}{\tan {45}^0}$
or, $\frac{i_1}{i_2}=\frac{\frac{1}{\sqrt{3}}}{1}$
or, $i_1:i_2=1:\sqrt{3}$