Question

an electric current in a conductor varies with time according to the expression I(t) = 100 sin (120pi*t), where I is in amperes and t in seconds. what is the total charge passing a given point in the conductor from t=0 to t=1/240s?

Answer 1

The total charge passing a given point in the conductor

$$q=\int_{t_1}^{t_2}i(t)dt=\\ =100\int_{0}^{1/240}\sin(120\pi t)dt=\frac{100}{120\pi}=0.27\:\rm C.$$