A precision function generator drives a current I(t) through a coil according to the sinusoidal relation I(t)=Ipeaksin(ωt), starting at t=0.
• The peak current Ipeak is 2.5 A.
• The angular frequency ω is 120πrads−1 (corresponding to a 60 Hz power signal).
(a) Derive an algebraic expression for the total charge q(t) that has passed through the coil from time t=0 up to an arbitrary time t.
(b) Using your result from part (a), calculate the exact amount of charge that passes through the coil during the first quarter of a complete cycle.
(c) Determine the earliest time t1C at which exactly 1.0C of charge has passed through the coil.
(d) Over a full cycle (period T), what is the net charge transported through the coil? Explain physically why this result makes sense in the context of alternating current.