Q90 / 120 · VITEEE 2006 · Physics

In a tangent galvanometer, a current of $1 \mathrm{~A}$ produces a deflection of $30^{\circ}$. The current required to produce a deflection of $60^{\circ}$ is

  • Correct answer
    A
    $3 \mathrm{~A}$
  • B
    $2 \mathrm{~A}$
  • C
    $4 \mathrm{~A}$
  • D
    $1 \mathrm{~A}$

Solution

Current in tangent galvanometer $\mathrm{I}=\frac{\mathrm{H}}{\mathrm{G}} \tan \theta$ Where $\mathrm{G}=$ galvanometer constant $\mathrm{H}=\text { earth's horizontal field }=\text { constant }$ $\therefore \frac{\mathrm{I}_{1}}{\mathrm{I}_{2}}=\frac{\tan \theta_{1}}{\tan \theta_{2}} \Rightarrow \frac{1}{\mathrm{I}_{2}}=\frac{\tan 30^{\circ}}{\tan 60^{\circ}}$ $\begin{array}{l} \Rightarrow \mathrm{I}_{2}=\frac{\tan 60^{\circ}}{\tan 30^{\circ}}=\frac{1.7321}{0.5774}=2.999 Å \\ \Rightarrow \mathrm{I}_{2} \simeq 3 \mathrm{~A} \end{array}$

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

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