Q144 / 180 · COMEDK 2018 · Physics

Two tangent galvanometers $A$ and $B$ are identical except in their number of turns. They are connected in series. On passing a current through them, deflections of $60^{\circ}$ and $30^{\circ}$ are produce(d)The ratio of the number of turns in $A$ and $B$ is

  • A
    $1: 3$
  • Correct answer
    B
    $3: 1$
  • C
    $1: 2$
  • D
    $2: 1$

Solution

Given, $\theta_{A}=60^{\circ}, \theta_{B}=30^{\circ}$ We know that, deflection in galvanometer $\theta$ and current $I$ are related as $\tan \theta=K N I$ where, $K=$ constant, $N=$ number of turns in the coil of galvanometer and $I=$ current. $\therefore \quad \frac{\tan \theta_{A}}{\tan \theta_{B}}=\frac{N_{A}}{N_{B}}$ $\Rightarrow \quad \frac{\tan 60^{\circ}}{\tan 30^{\circ}}=\frac{N_{\mathrm{A}}}{N_{B}}$ $\Rightarrow \quad \frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=\frac{N_{A}}{N_{B}}$ $\Rightarrow \quad \frac{3}{1}=\frac{N_{A}}{N_{B}}$ $\Rightarrow \quad N_{A}: N_{B}=3: 1$

Hence, the correct answer is option: 'B'.

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