Question

In a tangent galvanometer, a current of 1A produces a deflection of 30?. The current required to produce a deflection of 60? is

• A. 3A
• B. 2A
• C. 4A
• D. 1A

Answer 1

The Correct Option is A

The current in a tangent galvanometer is given by:

\(I = \frac{H}{G}\tan\theta\)

Here, \(H\) and \(G\) are constants, so:

\(I \propto \tan\theta\)

Therefore, for two different currents:

\(\frac{I_1}{I_2} = \frac{\tan\theta_1}{\tan\theta_2}\)

Given angles:

\(\theta_1 = 30^\circ,\; \theta_2 = 60^\circ\)

So:

\(\frac{I_1}{I_2} = \frac{\tan 30^\circ}{\tan 60^\circ} = \frac{1/\sqrt{3}}{\sqrt{3}} = \frac{1}{3}\)

Hence:

\(I_2 = 3 I_1\)

If \(I_1 = 1\,A\), then:

\(I_2 = 3\,A\)

Alternatively, directly using values:

\(\tan 30^\circ = 0.5774,\quad \tan 60^\circ = 1.7321\)

\(I_2 = \frac{1.7321}{0.5774} \approx 3\)

Therefore, the required current is \(3\,A\).