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Q.
If a current of 500 mA produces a deflection of $ 30^\circ $ in a tangent galvanometer, then the current that produces a deflection of $ 60^\circ $ is
If an electric current I is flowing through the coil of the tangent galvanometer and the magnetic needie gets deflected and comes to rest making an angie $ \theta $ with the direction of horizontaI component of earth's magnetic field H, then for the tangent galvanometer
$ I = K \tan \theta $
where K is the reduction factor of tangent galvanometer.
$ \therefore \, \frac{I_1}{I_2} = \frac{tan \,\theta_1}{\tan \theta_2} $
or $ \frac{500}{I_2} = \frac{\tan 30^\circ}{\tan 60^\circ}$ or $\frac{500}{I_2} = \frac{\bigg(\frac{1}{\sqrt{3}}\bigg)}{\sqrt{3}} $
or $ \frac{500}{I_2} = \frac{1}{3} $
or $ I_2 = 1500 \,mA = 1.5\, A $