An electric current is given by the expression $I (t) = 100 \sin (120 πt)$ , where $I$ is in ampere and $t$ is in second. What is the total charge carried by the current from $t = 0$ to $t = (\frac{1}{240}) s$ ?

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$0.265 C$

$0.564 C$

$0.9 C$

$0.457 C$

answer is A.

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Detailed Solution

$I = \frac{d q}{d t} q = \int d q = \int I d t = \int_{0}^{\frac{1}{240} s} (100 A) \sin (\frac{120 πt}{s}) d t q = \frac{- 100 C}{120 π} [\cos (\frac{π}{2}) - \cos 0] = \frac{+ 100 C}{120 π} = 0.265 C$

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