Question

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

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

Answer 1

The correct option is C $5\sqrt{3/2}A$

Formula used:

$I=I_0\sin \omega t$,

$I_0=\sqrt{2}{I}_{rms}$

Given, Frequency, $v=50Hz$

$I_{rms}=5A$,

$t=\frac{1}{300}s$

As we know, $\frac{I_0}{\sqrt{2}}=I_{rms}$

Where, $I_0=$peak current

$I_0={\sqrt{2I}}_{rms}=\sqrt{2}\times 5A$

Since,

$I=I_0\sin \omega t$

$I=5\sqrt{2}\sin 100\pi \times \frac{1}{300}$

$=5\sqrt{2}\sin \frac{\pi }{3}$

$=5\sqrt{2}\times \frac{\sqrt{3}}{2}$

$I=5\sqrt{\frac{3}{2}}A$

Final Answer: $5\sqrt{\frac{3}{2}}A$