Question

Two tangent galvanometer $A$ and $B$ have coils of radii $8cm$ and $16cm$ respectively and resistance $8\Omega$ each. They are connected in parallel with a cell of emf $4V$ and negligible internal resistance. The deflections produced in the tangent galvanometer $A$ and $B$ are ${30}^{\circ }$ and ${60}^{\circ }$ respectively. If $A$ has $2$ turns, then $B$ must have :

• A. $18turns$
• B. $12turns$
• C. $6turns$
• D. $2turns$

Answer 1

The correct option is B $12turns$

Current in tangent galvanometer
$I=\frac{2rH}{{\mu }_{0}N}\tan \theta .....\left(i\right)$
Here, $R_1$ and $R_2$ are in parallel
$\therefore \frac{1}{R_{net}}=\frac{1}{R_1}+\frac{1}{R_2}$
$R_{net}=\frac{R_2+R_1}{R_1{R}_2}=\frac{8+8}{8\times 8}$
$R_{net}=4\Omega$
Hence, $I=\frac{V}{R}=\frac{4}{4}=1A$
From Eq. (i), we get
$\frac{r\tan \theta }{N}=\frac{{\mu }_{0}I}{2H}$

Since same current flows through both galvanometers, thus we get
$\therefore \frac{r_A\tan {\theta }_A}{N_A}=\frac{r_B\tan {\theta }_B}{N_B}$
$\Rightarrow \frac{8\times 1}{\sqrt{3}\times 2}=\frac{16\times \sqrt{3}}{N_B}$
$\therefore N_B=12turns$.