JEE MAIN - Physics (2022 - 28th July Morning Shift - No. 13)
The equation of current in a purely inductive circuit is $$5 \sin \left(49\, \pi t-30^{\circ}\right)$$. If the inductance is $$30 \,\mathrm{mH}$$ then the equation for the voltage across the inductor, will be :
$$\left\{\right.$$ Let $$\left.\pi=\frac{22}{7}\right\}$$
$$1.47 \sin \left(49 \pi t-30^{\circ}\right)$$
$$1.47 \sin \left(49 \pi t+60^{\circ}\right)$$
$$23.1 \sin \left(49 \pi t-30^{\circ}\right)$$
$$23.1 \sin \left(49 \pi t+60^{\circ}\right)$$
Explanation
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$$V(t) = I\omega L\sin (49\pi t - 30^\circ + 90^\circ )$$
$$ = 5 \times 49\pi \times {{30} \over {1000}}\sin (49\pi t + 60^\circ )$$
$$ = 23.1\sin (49\pi t + 60^\circ )$$
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