how a phase delay occurs in capacitors/inductors with visual images
Alas, most educators seem to focus on rote memorization of equations, rather than intuition and understanding.
The best "intuitive" explanation of capacitors I've seen so far comes from William Beaty. Here is an image from that explanation:



Beaty talks a lot about how things really work, and distinguishes between the Euclidean or "Greek viewpoint" involving memorizing equations; vs. the "Babylonian viewpoint" where concepts are far more important than equations. He tries to get pictures and analogies to give a visual and gut-level understanding of something.( a )

Most such "intuitive" descriptions of electric devices use a hydraulic analogy.

With both capacitors and inductors, energy can be stored "in" the device.
Often we rapidly go back and forth between pumping energy into the device and pulling the energy back out of the device.

Whenever we have something in a box that stores something -- energy, rice, water, marbles, etc. -- and whenever we go back and forth between gradually putting something into the box and gradually taking something out of the box -- the peaks (maximum) of the "amount of stuff in the box" always lag the start of putting something into the box. Also, the lowest point in the valleys (minimum) "amount of stuff in the box" always lag the start of taking stuff out of the box.
The time when we have the maximum amount of stuff in that box happens at the instant we stop putting stuff into the box, and start taking stuff out of the box.

We add more energy to a capacitor by pushing electrons in one side (and pulling the same number of electrons out the other side). The voltage ("pressure") across the capacitor can be used to calculate how much energy is stored in the capacitor.

We add more energy to an inductor by forcing an electromotive force across its terminals.
The flow of electrons ("current") through the inductor can be used to calculate how much energy is stored "in" the inductor.