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 $B =\frac{\mu_{0} nI }{2 a }$
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.
$B _{1}=\frac{\mu_{0} n _{1} I }{2 a }= B _{ h } \tan \theta_{1} \ldots (i)$
$B _{2}=\frac{\mu_{0} n _{2} I }{2 a }= B _{ h } \tan \theta_{2} \ldots(ii)$
$\frac{ B _{1}}{ B _{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}$
$\frac{ n _{1}}{ n _{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}}$
$\frac{ n _{1}}{ n _{2}}=\frac{\tan 60}{\tan 45}$
$\frac{ n _{1}}{ n _{2}}=\frac{\sqrt{3}}{1}$