Question

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

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

Answer 1

Answer: (D)

$\frac{\sqrt{3}}{1}$

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 $B=\frac{{\mu }_{\circ }nI}{2a}$

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.

$B_1=\frac{{\mu }_{\circ }{n}_{1}I}{2a}=B_h\tan {\theta }_1$....(i)

$B_2=\frac{{\mu }_{\circ }{n}_{2}I}{2a}=B_h\tan {\theta }_2$....(ii)

$\frac{B_1}{B_2}=\frac{\tan {\theta }_1}{\tan {\theta }_2}$

$\frac{n_1}{n_2}=\frac{\tan {\theta }_1}{\tan {\theta }_2}$

$\frac{n_1}{n_2}=\frac{\tan 60}{\tan 45}$

$\frac{n_1}{n_2}=\frac{\sqrt{3}}{1}$ .