Q140 / 180 · KCET 2013 · Physics

Two tangent galvanometers, which are identical except in their number of turns, are connected in parallel. The ratio of their resistances of the coils is 1 : 3 . If the deflections in the two tangent galvanometers are $30^{\circ}$ and $60^{\circ}$ respectively, then the ratio of their number of turns is

  • A
    $1: 1$
  • B
    $3: 1$
  • C
    $1: 2$
  • Correct answer
    D
    $1: 6$

Solution

We know that the current passing through galvanometer coil is $I=K \tan \theta$ where $K=\frac{2 r B_{H}}{n \mu_{0}}$ $\therefore$ Here, $\quad I_{1}=K_{1} \tan \theta_{1}$ and $I_{2}=K_{2} \tan \theta_{2}$ or $\quad \frac{l_{1}}{I_{2}}=\frac{K_{1} \tan \theta_{1}}{K_{2} \tan \theta_{2}}=\frac{\frac{2 r B_{H}}{n_{1} \mu_{0}} \tan \theta_{1}}{\frac{2 r B_{H}}{n_{2} \mu_{0}} \tan \theta_{2}}$ $\Rightarrow \quad \frac{R_{2}}{R_{1}}=\frac{n_{2} \tan 30^{\circ}}{n_{1} \tan 60^{\circ}}$ $\Rightarrow \quad \frac{3}{1}=\frac{n_{2}}{n_{1}} \cdot \frac{\sqrt{3}}{\sqrt{3}} \quad\left(\because I=\frac{V}{R}\right)$ $\Rightarrow \quad \frac{n_{1}}{n_{2}}=\frac{1}{3}$

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

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