Question

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

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

Hint:

In tangent galvanometer, $I \propto \tan\theta$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
For tangent galvanometer, $I \propto \tan\theta$.
Step 2: Detailed Explanation:
$I_1 = \frac{12}{4+2} = 2$ A, $\tan 60^{\circ} = \sqrt{3}$. $I_2 \propto \tan 30^{\circ} = \frac{1}{\sqrt{3}}$. So $\frac{I_2}{I_1} = \frac{1/\sqrt{3}}{\sqrt{3}} = \frac{1}{3}$, hence $I_2 = \frac{2}{3}$ A. Then $\frac{12}{4+2+R} = \frac{2}{3} \Rightarrow 12 = \frac{2}{3}(6+R) \Rightarrow 18 = 6+R \Rightarrow R = 12\Omega$.
Step 3: Final Answer:
The resistance to be connected is $12\Omega$.