Question

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

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

Answer 1

Answer: (B)

12 turns

Answer 2

Current in tangent glavanometer $I=\frac{2rH}{{{\mu }_{0}}N}\tan \theta$ ...(i) Here, ${{R}_{1}}$ and ${{R}_{2}}$ are in 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, $I=\frac{V}{R}=\frac{4}{4}=1\,A$ From E (i), we get $\frac{r\tan \theta }{N}=\frac{{{\mu }_{0}}I}{2H}$ $\therefore$ $\frac{{{r}_{A}}\tan {{\theta }_{A}}}{{{N}_{A}}}=\frac{{{r}_{B}}\tan {{\theta }_{B}}}{{{N}_{B}}}$ $\Rightarrow$ $\frac{8\times 1}{\sqrt{3}\times 2}=\frac{16\times \sqrt{3}}{{{N}_{B}}}$ $\therefore$ ${{N}_{B}}=12\,turns$