Question

Two tangent galvanometer having coils of the same radius are connected in series. A current flowing in them produces deflection of $60^{\circ }$ and $45^{\circ }$ respectively. The ratio of the number of turns in the coils is

• A. $4/3$
• B. $(\sqrt{3}+1)/1$
• C. $\sqrt{3}/1$
• D. $(\sqrt{3}+1)/(\sqrt{3}-1)$

Answer 1

Answer: (C)

Tangent galvanometer is an early measuring instrument for small electric currents. It consists of a coil of insulated copper wire wound on a circular non-magnetic frame. Its working is based on the principle of the tangent law of magnetism. When a current is passed through the circular coil, a magnetic field $(B)$ is produced at the center of the coil in a direction perpendicular to the plane of the coil. The $TG$ is arranged in such a way that the horizontal component of earth’s magnetic field $(B_h)$ is in the direction of the plane of the coil. The magnetic needle is then under the action of two mutually perpendicular fields. If θ is the deflection of the needle, then according to tangent law,
$B=B_h\tan \theta$
where $B=\frac{{\mu }_{0}nI}{2a}$
Where n is number of coils, $I$ is current and a is radius of coil.
Given radius of both coils are same.
The current will be same as both coils are connected in series.
$B_1=\frac{{\mu }_0{n}_{1}I}{2a}=B_h\tan {\theta }_1\dots (i)$
$B_2=\frac{{\mu }_0{n}_{2}I}{2a}=B_h\tan {\theta }_2\dots (ii)$
$\frac{B_1}{B_2}=\frac{\tan {\theta }_1}{\tan {\theta }_2}$
$\frac{n_1}{n_2}=\frac{\tan {\theta }_1}{\tan {\theta }_2}$
$\frac{n_1}{n_2}=\frac{\tan 60}{\tan 45}$
$\frac{n_1}{n_2}=\frac{\sqrt{3}}{1}$