An AC current is given by the expression,I(t) | vedclass

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(B) The standard equation for an alternating current is given by $I(t) = I_0 \sin(\omega t)$,where $I_0$ is the peak current and $\omega$ is the angul

Vedclass · Accepted Answer

$100 	ext{ Hz}, 25 \sqrt{2} 	ext{ A}$

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(B) The standard equation for an alternating current is given by $I(t) = I_0 \sin(\omega t)$,where $I_0$ is the peak current and $\omega$ is the angular frequency.Comparing this with the given equation $I(t) = 50 \sin(200 \pi t)$,we find the peak current $I_0 = 50 	ext{ A}$ and the angular frequency $\omega = 200 \pi 	ext{ rad/s}$.The $RMS$ value of the current is calculated as $I_{RMS} = \frac{I_0}{\sqrt{2}} = \frac{50}{\sqrt{2}} = 25 \sqrt{2} 	ext{ A}$.The frequency $f$ is related to the angular frequency by the formula $\omega = 2 \pi f$.Substituting the value of $\omega$,we get $200 \pi = 2 \pi f$,which simplifies to $f = 100 	ext{ Hz}$.Thus,the frequency is $100 	ext{ Hz}$ and the $RMS$ value is $25 \sqrt{2} 	ext{ A}$.

An $AC$ current is given by the expression,$I(t) = 50 \sin(200 \pi t)$ in amperes. The frequency and $RMS$ value of the current respectively are

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