The instantaneous value of an alternating current is given by $\mathrm{I}=50 \sin (100 \pi \mathrm{t})$. It…

The instantaneous value of an alternating current is given by $\mathrm{I}=50 \sin (100 \pi \mathrm{t})$. It will achieve a value of $25 \mathrm{~A}$ after a time interval of $\left(\sin 30^{\circ}=0.5\right)$
  1. $\frac{1}{300} \mathrm{~S}$
  2. $\frac{1}{100} \mathrm{~S}$
  3. $\frac{1}{200} \mathrm{~S}$
  4. $\frac{1}{600} \mathrm{~S}$

Solution

$\begin{aligned} & \mathrm{i}=50 \sin 100 \pi \mathrm{t} \\ & \therefore 25=50 \sin 100 \pi \mathrm{t} \\ & \frac{25}{50}=\sin 100 \pi \mathrm{t} \\ & \frac{1}{2}=\sin 100 \pi \mathrm{t} \\ & 100 \pi \mathrm{t}=\frac{\pi}{6} \\ & \therefore \mathrm{t}=\frac{1}{600} \mathrm{~S}\end{aligned}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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