How can voltage be zero when current is non zero? (Single phase series circuits)
Isn't it clear that in AC circuits, the voltage swings both positive and negative continually, and so does the current?

So, there always has to be an instant between positive voltage and negative voltage when the voltage is zero, no matter how brief. Same thing for current.

With resistors, voltage and current are always proportional to each other, so they have to be zero at the same time. Inductors and capacitors store energy, so the voltage zero and the current zero do NOT have to occur at the same time &mdash; and in most cases, they cannot occur at the same time.

The governing equations are

$$V(t) = L\frac{dI(t)}{dt}$$

and

$$I(t) = C\frac{dV(t)}{dt}$$

Loosely translated, the voltage on a coil is proportional to the rate of change of the current through it, and the current through a capacitor is proportional to the rate of change of voltage across it. Continuous sine waves (and cosine waves) constitute just one of many possible solutions to this set of differential equations, and their zeros are 90&deg; apart.