Q 12-07-109JEE MainJEE Main 2022 (28 Jul, Shift 1)Medium
The equation of current in a purely inductive circuit is $5\sin(49\pi t - 30^\circ)$. If the inductance is $30$ mH then the equation for the voltage across the inductor, will be
Answer: (D) $23.1\sin(49\pi t + 60^\circ)$
$$X_L = \omega L = 49\pi\times0.03 \approx 4.62\ \Omega, \qquad V_0 = I_0X_L = 5\times4.62 \approx 23.1\ \text{V}$$
In a pure inductor the voltage leads the current by $90^\circ$:
$$V = 23.1\sin(49\pi t - 30^\circ + 90^\circ) = 23.1\sin(49\pi t + 60^\circ)$$
Solution by Sreeraj P, M.Sc Physics