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JEE Main
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Physics
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Experimental Physics

JEE Main · Physics · Experimental Physics

A battery of emf 12V and internal resistance 2Ω is connected in...

A battery of emf 12V12V and internal resistance 2Ω2Ω is connected in series with a tangent galvanometer of resistance 4Ω.4Ω . The deflection is 60o{60}^{o} when the plane of the coil is along the magnetic meridian. To get a deflection of 30o,{30}^{o}, the resistance to be connected in series with the tangent galvanometer is

Options

  1. A12Ω12Ω
  2. B20Ω20Ω
  3. C10Ω10Ω
  4. D5Ω5Ω

Correct answer

A. 12Ω12Ω

Step-by-step solution

I=ktanθ,kI = ktan \theta,k being reduction factor and I∝1RI ∝ \dfrac{1}{R}

⇒R+r(R+r)+R′=tanθ′tanθ⇒ \dfrac{R + r}{\left(R + r\right) + R^{′}} = \dfrac{tan {\theta}^{′}}{tan \theta}

⇒4+26+R′=tan30otan60o⇒ \dfrac{4 + 2}{6 + R^{′}} = \dfrac{tan {30}^{o}}{tan {60}^{o}}

⇒R′=12Ω⇒ R^{′} = 12Ω
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