Q141 / 170 · Manipal (MET) 2018 · Physics

A battery of emf 12 V and internal resistance $2 \Omega$ is connected in series with a tangent galvanometer of resistance $4 \Omega$. The deflection is $60^{\circ}$ when the plane of the coil is along the magnetic meridian. To get a deflection of $30^{\circ}$, the resistance to be connected in series with the tangent galvanometer is

  • Correct answer
    A
    $12 \Omega$
  • B
    $20 \Omega$
  • C
    $10 \Omega$
  • D
    $5 \Omega$

Solution

$I=k \tan \theta, k$ being reduction factor and $I \propto \frac{1}{R}$ $\begin{aligned} & \Rightarrow \frac{R+r}{(R+r)+R^{\prime}} =\frac{\tan \theta^{\prime}}{\tan \theta} \\ & \Rightarrow \frac{4+2}{6+R^{\prime}} =\frac{\tan 30^{\circ}}{\tan 60^{\circ}} \\ & \Rightarrow R^{\prime} =12 \Omega \end{aligned}$

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

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