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  4. Alternating current in an AC circuit varies with time as i(t) = 100 sin 50πt cos 50πt. The maximum current and frequency are respectively (i is in ampere and t is in second)

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Q. Alternating current in an AC circuit varies with time as i(t) = 100 sin 50$\pi$t cos 50$\pi$t. The maximum current and frequency are respectively (i is in ampere and t is in second)

Solution:

$i(t) = 100 sin 50\pi t cos 50\pi t$
$= 50(2sin\, 50\pi t cos 50\pi t)$
$= 50 sin(100 \pi t)$
$I_o = 50 A\, and \, f =\frac{100 \pi}{2\pi}=50\,Hz$