Question

An electric current in a conductor varies with time according to the expression I(t) = 118 sin (180𝜋t), where I is in amperes and t is in seconds. What is the total charge passing a given point in the conductor from t = 0 to t = 1/240 s?

Answer 1

To obtain the total charge we should calculate the integral of the current over time

$\int\limits_{0}^{1/240\, \text{s}} 118\sin (180\pi t)\,dt = -\dfrac{118}{180\pi}\cos(180\pi t)\Big|_{0}^{1/240\,\text{s}} =- \dfrac{118}{180\pi}\cdot (\cos(3/4 \pi)-\cos 0) = \dfrac{118}{180\pi}\cdot (1 + \sqrt{2}/2 ) \approx 0.356\,\mathrm{C}.$