Question

The deflection of the magnetic needle in a tangent galvanometer is ${30}^{\circ }$ when a current of one ampere flows through it. The deflection of the magnetometer when a current of $4A$ flows through it is:

• A. ${tan}^{-1}\left(8.7\right)$
• B. ${tan}^{-1}\left(2.31\right)$
• C. ${tan}^{-1}\left(1.73\right)$
• D. ${tan}^{-1}\left(\sqrt{2}\right)$

Answer 1

The correct option is B ${tan}^{-1}\left(2.31\right)$

Since the current in galvanometer is proportional to $tan\theta$, $\theta$ being the deflection
Hence, in second case, deflection will be :
$\frac{1}{4}=\frac{B_{H}tan\left({30}^0\right)}{B_{H}tan\theta }$

$\theta ={tan}^{-1}\left(4tan\right({30}^0\left)\right)=ta{n}^{-1}\left(\frac{4}{\sqrt{3}}\right)={tan}^{-1}\left(2.31\right)$