Question

When $\sqrt{3}$ ampere current is passed in a tangent galvanometer, there is a deflection of ${30}^{\circ }$ in it. The deflection (in degree) obtained when $3$ amperes current is passed, is

Answer 1

For a tangent galvanometer, if deflection $=\theta$, the current reading is given by

$i=k\tan \theta$

Where, $k=\frac{2r{B}_H}{{\mu }_{0}n}=$ reduction factor of galvanometer

$n=\text{no. of turns in the coil,}r=\text{radius of the coil}$

$\frac{i_1}{i_2}=\frac{\tan {\theta }_1}{\tan {\theta }_2}$

$\frac{\sqrt{3}A}{3A}=\frac{\tan {30}^{\circ }}{\tan {\theta }_2}$

$\tan {\theta }_2=1$

${\theta }_2={45}^{\circ }$

Thus, deflection obtain for $3A$ current is ${45}^{\circ }$