Question

If the rms current in a $50\, Hz$ ac circuit is $5\, A$, the value of the current $1/300$ seconds after its value becomes zero is

• A. $5\sqrt{2}\,A$
• B. $5\sqrt{\frac{3}{2}}\,A$
• C. $\frac{5}{6}\,A$
• D. $\frac{5}{\sqrt{2}}\,A$

Answer 1

Answer: (B)

Here, $I_{rms} = 5\,A$, $\upsilon = 50\,Hz$,
$t=\frac{1}{300}\,s$
$I_{0}=\sqrt{2}\,I_{rms}=5\sqrt{2}\,A$,
$I=I_{0}\,sin\omega t=I_{0}\,sin2\pi\upsilon t=5\sqrt{2}\,sin\left(2\pi \times 50 \times \frac{1}{300}\right)$
$=5\sqrt{2}\,sin \frac{\pi}{3}$
$=5\sqrt{2} \frac{\sqrt{3}}{2}$
$=5\sqrt{\frac{3}{2}}\,A$