Q. Two tangent galvanometers A and B have coils of radii 8 cm and 16 cm respectively and resistance $8\ \Omega$ each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers A and B are $30{^\circ}\ and\ 60{^\circ}$ respectively. If A has 2 turns, then B must have
Explanation
(b) Current in tangent galvanometer
$I = \frac{2rB_{H}}{\mu_{0}N}\tan\theta\ \ \ \ \ \ \ \ \ \ \ ..(i)$
Here $R_{1}\ and\ R_{2}$ are parallel
$\therefore\ \ \ \ \ \ \ \ \ \frac{1}{R_{net}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{R_{2} + R_{1}}{R_{1}R_{2}} = \frac{8 + 8}{8 \times 8}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ R_{net} = 4\ \Omega$
Hence, $\ \ \ \ \ I = \frac{V}{R} = \frac{4}{4} = 1A$
From Eq. (i), we get
$\ \ \ \ \ \ \ \ \frac{r\tan\theta}{N} = \frac{\mu_{0}I}{2B_{H}}$
$\therefore\ \frac{r_{A}\tan\theta_{A}}{N_{A}} = \frac{r_{B}\tan{\theta_{B}}}{N_{B}}$
$\Rightarrow \ \ \ \ \ \ \frac{8 \times 1}{\sqrt{3}} = \frac{16}{N_{B}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ N_{B} = 12\ turns$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.